The night before, feed your sourdough starter 50g of water and 50g of flour.
Make The Dough (The Next Day)
Heat the liquid ingredients. In a microwave-safe bowl, microwave the milk and butter so that they are warm. The butter should be melted. You can also heat the milk and butter on a stovetop.
In the bowl of a stand mixer, add in the milk, butter, honey, and sourdough starter. Stir with a spatula to mix the liquid ingredients. The ingredients will not completely combine, and that's okay.
Mix. In the bowl of a stand mixer, slowly add in 3 ½ cups of flour. Use the dough hook attachment on medium-low to medium speed until the ingredients are combined. The dough should be slightly sticky to the touch but not too sticky. If the dough is too sticky, add ¼ cup of flour. Mix in the bowl of a stand mixer for roughly 10 minutes or until the dough is smooth.
First Rise: Place the dough ball in an oiled container and cover. Allow the dough to rise for 2 to 4 hours or until it has risen by 50% (Check notes.)
Shape: Place the dough ball on a floured surface. Divide the dough ball into 15 equal pieces. To shape, press one piece of dough into a flat square. Pinch the corners and the sides of the dough toward the middle. Turn the dough over so that the seam side is down and touching the work surface. Gently form into a smooth ball.
Second Rise: Grease a 9 x 13-inch baking dish with oil. Place the dough balls into the dish and evenly space them apart. Cover and let rise for 2-4 hours or until doubled in size. (Check Notes).
Bake: Before baking, brush each dough ball with egg wash (1 whole egg plus a splash of milk). Bake uncovered at 375F for 20 to 25 minutes or until they are golden brown. Brush the top of the sourdough dinner rolls with melted butter and serve.
Notes
Watch the dough, NOT the clock! Doughs will rise slower or faster depending on the temperature and environment. For instance, if your kitchen is cold (50F), your dough may rise slower. In that case, you would have to increase the time for the first rise and second rise.
Try to keep the dough at a warm temperature. This will ensure that your dough rises at a decent time.
Make sure your active starter doubles within four hours after feeding. If it does not, then that means that your sourdough starter is weak and cannot reliably raise bread.
You can make the dough the day before and bake them tomorrow. After shaping the dough ball into rolls, place in the baking pan and cover. Place in the fridge overnight during its second rise (also called final rise or proofing). You can bake them straight from the fridge.