(See note above about rise time before beginning). Combine starter, warm water, sugar or honey, butter, egg, egg yolk, salt, and about 2 cups/250g of flour in a large mixing bowl or the bowl of a stand mixer fitted with a dough hook. Stir until well-combined.
Gradually, while stirring, add remaining flour until the dough is clinging to itself and pulling away from the sides of the bowl. Add additional flour as needed; dough should be soft, sticky/tacky but should cling to itself and shouldn’t come off on your fingertip if gently prodded.
If using a stand mixer (preferred/recommended), use the dough hook to knead dough until smooth and elastic (about 5-10 minutes on medium/low speed). If preparing by hand, transfer to a lightly floured surface and knead until smooth and elastic (about 10 minutes, you will likely have to add more flour as you go).
Place dough in a lightly oiled bowl (I use olive or avocado oil), cover with plastic wrap, and allow to rise for 5-8 hours, until nearly doubled in size. Transfer to refrigerator and allow to rest/ferment overnight.
The next dayGenerously grease a 13×9 glass or ceramic baking dish with butter. Set aside.
Remove dough from the refrigerator and turn dough out onto a lightly floured surface. Dough will be cold and dense, this is perfect for best handling.
Divide dough into 15 (for larger rolls) or 20 (for smaller rolls) even pieces and gently roll each into a smooth ball.
Space dough balls evenly into prepared baking dish. Cover with plastic wrap and allow to sit in a warm, draft-free space until rolls are puffed and touching. Rolls should pass the poke test, meaning if gently poked with a lightly floured finger they will spring back halfway. If the dough springs back all the way it needs more time (and if it doesn’t spring back at all, they’re unfortunately overproofed, bake them anyway). This usually takes about 1 ½-2 hours in my kitchen but will vary. When rolls are nearly finished rising, preheat oven to 375F (190C).
Uncover rolls and, if desired, use a pastry brush to lightly brush the surface of each roll with an egg wash made by whisking together 1 egg with 1 teaspoon of water or milk.
Transfer rolls to center rack of 375F (190C) oven and bake for 20-30 minutes (if baking 20 rolls you’ll need to start checking at 20 minutes, if baking 15 rolls they typically take 25-30 minutes). Rolls should be turning light golden on top and an instant-read thermometer inserted in the center of a roll should reach 185-190F (85-88C).
Serve warm, though they’re delicious at room temperature and reheat well, too!