Place milk, 4 eggs, the flour and yeast in the bowl of a stand mixer fitted with the dough hook attachment. Mix on medium speed until dough is smooth and comes together, about 3 minutes, scraping down the bowl after the first minute of mixing, if needed. Let dough rest in bowl 20 minutes to help relax the gluten.

Add sugar and salt; mix on low speed 3 minutes more, scraping dough off the hook after the first minute.

Add half of the butter and continue to mix on low until butter cubes are no longer visible and are completely incorporated into dough. Add remaining butter and mix until incorporated.

After all the butter is added into the dough, add chopped rosemary and thyme. Continue mixing dough on medium speed until it makes a slapping sound and dough comes away from the bowl, about 16 minutes. Be patient and resist the urge to increase the speed. You will start hearing a distinct slapping sound when dough is almost ready.

Remove dough from bowl and gently knead with your hands, about 1 minute. Return dough to bowl, cover with plastic wrap and let sit 45 minutes. Punch down dough to help redistribute the yeast. Cover again and refrigerate at least 2 hours or overnight.

To shape rolls: Grease a 9x13-inch cake pan or two 10-inch cast-iron skillets. Transfer dough to a work surface and divide into 18 equal balls. (If you have a kitchen scale, they will weigh about 55 g apiece.) Take each ball and place in the palm of your hand. Round them on the counter to create skin tension, lightly flouring your hand as needed. Arrange balls of dough in pan, spacing them about 1/4 inch apart. Loosely cover with plastic wrap.

Preheat oven to lowest setting, about 170°. Place another cake pan on lowest oven rack. Add 1 cup boiling water to cake pan. Turn off oven. Place pan with rolls on center oven rack. Let proof until slightly risen and nearly touching, 11/2 to 21/2 hours.

Remove all pans from oven. Preheat oven to 350°. Remove plastic wrap from rolls. Bake until golden brown, about 20 minutes, rotating pan halfway through baking.

Meanwhile, place rosemary sprig and butter in a small microwaveable bowl or saucepan. Microwave or warm over low heat to melt. Brush hot, baked rolls with butter. Let cool 10 minutes and serve warm. (Or, to make ahead, let cool completely, cover with plastic wrap, and serve the next day. The rolls can be frozen for up to 3 months. Rewarm frozen rolls in oven at 350° for 10 minutes, then brush with butter and serve warm. Once reheated, they are best eaten that day.)