In the bowl of your stand mixer (or a large mixing bowl), add the sweet levain, milk, sugar, honey, egg, and egg yolks. Whisk ingredients together quickly, it's okay if it's lumpy.
3/4 (200g) cup sweet levain, 1 (200g) cup whole milk, 1/3 (75g) cup granulated white sugar, 2(40g) Tbspns raw honey, 1 (50g) large egg, 2 (36g) egg yolks
Add the flour and salt to the wet ingredients.
4 1/4 (550g) cups all-purpose flour, 1 1/2 (10g) teaspoon sea salt
Mix on low speed or Speed 1 until a shaggy dough forms, about 2-3 minutes. Scrape down the bowl if needed. If using your hands, knead until you work the dough together. This is a higher hydration dough, so be aware it will be sticky.
Once the dough has come together add the 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.
8 (113g) Tablespoons unsalted butter
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.
Mixing Notes: If kneading in a mixer or if dough is very wet when mixing by hand, add an additional 25 grams (3 Tablespoons) of flour and mix into dough. Make sure to work flour in completely and assess if you need more flour.
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.