Before you get started on mixing your dough, you'll make your tangzhong. Whisk milk and flour together in a small saucepan.

Cook the tangzhong over medium/low heat, stirring constantly, until it thickens into a paste that is similar to pudding (about 2–3 minutes). For precision, use your digital thermometer and heat to 148-155 F. Do not overheat, or your mixture will be too thick.

Scrape into a bowl immediately to prevent further cooking, cover, and let cool to room temperature before adding to your dough.

Prepare your dough while tangzhong cools.

In a stand mixer fitted with a dough hook or large mixing bowl, add all of the tangzhong, whole milk, sourdough discard or starter, instant yeast, eggs, sugar, and vanilla. Whisk ingredients together quickly, it's okay if it's lumpy.

Mix on low until a shaggy dough forms, about 2-3 minutes. Scrape down bowl if needed. If using your hands, knead until you work dough together. This is a higher hydration dough, so be aware it will be sticky.

Once the dough has come together add softened butter, a tablespoon at a time mixing each tablespoon in until adding the next. Use a dough scraper to scrape the edges of the bowl to make sure everything is getting mixed in.

Continue mixing on medium-low (speed 2–3) for 8–10 minutes, until dough is smooth, elastic, and tacky but not sticky.

If mixing by hand, knead dough until butter has fully incorporated and dough is smooth and tacky.

Do not add more than 50 grams of flour at this stage, or you will lose the high hydration of the dough and end up with a dense dough. If using a stand mixer, dough can become more warm and sticky and I have found kneading dough with my hand (perform a set of stretch and folds) for a minute after mixing in my stand mixer really helps bring the dough together.

Spray a clean mixing bowl large enough for the dough to double in size with cooking spray, and transfer the dough to the bowl covering it with a lint-free kitchen towel or lid. Allow the dough to rest 20 minutes.

After the 20 minute rest, knead the dough by hand for a minute or two to get the dough even softer and to work the gluten. Once you've finished this kneading step, cover the bowl again.

Allow the dough to rest about 1 1/2 hours at room temperature and the dough is ~75–90% risen. You don't want this dough to proof double fully at this rising point.

If the dough proofs sooner than the time I mentioned, shape it. You want to watch the dough to make sure it doesn't overproof at this stage!

While the dough is rising, make your filling.

Wash your apples and dry them. Peel and chop them into 1/4 inch cubes (this is key to getting the apples properly cooked). Transfer the apples to a large mixing bowl.

Add the lemon juice, white sugar, brown sugar, cinnamon, cardamom, vanilla, salt, cream, and flour to the bowl; toss the apple chunks with filling ingredients until they're coated.

In a saucepan over medium heat, melt your butter. When the butter has melted, add the apple filling. Cook the apples for about 8-10 minutes, until the apples are soft and a caramel sauce has formed.

Make sure to keep stirring the apples off of the bottom of the pan to avoid burning. Transfer the filling to a bowl to cool.

Once the filling has cooled, it should be thick and spoonable. You want the filling fully cooled before you add it to the center of the buns. You can refrigerate the apple filling until you're ready to assemble your buns.

Melt the butter in a microwave safe bowl, then add the flour, white sugar, brown sugar, cinnamon, and salt. Combine the crumble until its clumpy and crumbly. Set aside for later.

Make sure your cream cheese is completely softened before mixing the cream cheese filling.

Add the softened cream cheese and sugar to a medium bowl. Beat with a hand mixer for 2–3 minutes on high, until smooth and creamy.

Add the egg yolk, vanilla, flour, and salt to the cream cheese mixture. Beat on medium speed until combined.

Transfer the cream cheese filling to a piping bag or zip-top bag and chill for 15–20 minutes while the dough finishes rising.

The short chill makes the filling easier to pipe and helps it stay in the center of the buns.

Line 2 half size cookie sheets with parchment paper or silicone mats and spray lightly with cooking oil. Set side.

Grease a clean work surface with a little cooking spray, and transfer dough from bowl to counter. Weight out 9 dough balls (roughly 120 grams), and shape them into tight balls.

Transfer dough balls to prepared baking sheets and cover with oiled plastic wrap. Allow dough balls to proof about 1 hour at room temperature until puffy and almost doubled in size.

Don't skip this step for proofing; For a light and fluffy bun it's essential.

Prepare an egg wash with 1 egg and 2 teaspoons of water in a small bowl. Beat together until smooth and set aside.

Gather your apple pie filling, piping bag filled with cream cheese filling, and crumble.

Grease the back of a small glass or measuring cup or use your fingers to press a deep well in the center of each dough ball.

Snip about 1/4 inch off of the end of the bag filled with cream cheese filling. Pipe 2-3 Tablespoons of the cream cheese filling into each well in the center of the bun.

Spoon about 1-2 Tablespoons of the apple pie filling on the top of the cream cheese filling.

Brush the outside ring of the bun with the egg wash. You can do this with a paper towel or a pastry brush.

Sprinkle 2 teaspoons approximately of crumble around the edge of the bun where you brushed the egg wash.

Preheat your oven to 350°F (175°C).

Transfer the buns to the hot oven, and bake the buns for 25-30 minutes until golden brown and fillings are just set. Internal temperature should read around 195-200°F in bread portion of bun.

Avoid the cheesecake filling browning or cracking; if buns start to brown too much tent with foil if needed.

Cool on a wire rack for 15-20 minutes and allow the centers are set.

Enjoy!

Yields 9 Buns