Microwave milk, uncovered, until warm (90° to 105°), about 20 seconds at full power. Put in the bowl of a stand mixer. Stir in yeast, salt, and sugar. Let sit until foamy, about 5 minutes.
Attach dough hook and, with mixer on low, stir in butter and 1 egg. Add flour, 1/2 cup at a time, until a stiff dough forms and pulls away from inside of bowl. Cover with a clean towel or plastic wrap and let sit until doubled in bulk, about 1 1/2 hours. Meanwhile, butter 2 large baking sheets and set aside.
Punch down dough and turn it onto a floured surface. Knead a few times, adding more flour if necessary to keep dough from sticking. Divide dough into 24 pieces. Working with 1 piece at a time (keep other pieces covered), roll into a 10-in. rope. Coil rope into a flat spiral or twist into a pretzel shape, pinching ends in place. Put shaped rolls on buttered baking sheets. Cover and let sit until doubled in bulk, about 45 minutes. Meanwhile, preheat oven to 350°.
In a small bowl, beat remaining egg with 2 tbsp. water. Brush rolls with egg wash and bake until brown, about 20 minutes, rotating pans halfway through baking time to ensure even baking. Cool on wire racks. Serve warm or at room temperature.
Seed Rolls: After brushing rolls with egg wash in step 4, sprinkle them with 1 tbsp. poppy seeds, sesame seeds, or onion seeds.
Cheese Rolls: Add 1 1/2 cups freshly shredded cheddar or gruyère cheese to the dough with the butter and egg in step Sprinkle rolls with additional cheese before baking, if you like.
Herb Rolls: Add 3 tbsp. minced fresh herbs—such as oregano, rosemary, thyme, or basil—to the dough with the butter and egg in step
Saffron Rolls: Add 1/2 tsp. saffron threads to the milk in step
Note: Nutritional analysis is per roll.