Step 1

Butter a 15-by-10-by-1-inch jellyroll pan, then line it with parchment paper and butter the paper.

Step 2

In a small saucepan over medium heat, heat the butter, milk and sugar until the mixture registers about 130 degrees on an instant-read thermometer.

Step 3

In a stand mixer fitted with the paddle attachment, mix together 2 1/4 cups (281 grams) of the flour, the yeast and salt on low speed just until combined. Add the hot milk mixture and mix until combined and smooth, then mix on low speed until a smooth, loose dough has formed, about 2 minutes. Cover the bowl and let the dough rest for 10 minutes.

Step 4

With the mixer motor on low speed, add the eggs and mix until incorporated. Add the remaining scant 3 cups (359 grams) of flour and continue to mix for about 6 minutes. At first, the dough will look ragged, but it will become smooth after several minutes. By the end of the 6 minutes, it should be soft and pull away from the sides of the bowl.

Step 5

Using about 2 1/2 tablespoons (48 grams) dough for each roll, shape each portion (lightly flour your palms between each shaping, if necessary) into a smooth 1 3/4-inch ball. To encourage the best rise, try to form a "gluten cloak" by pulling the top of the dough down and around each ball before pinching and sealing around the bottom. Place the rolls on the prepared pan, spacing them about 3/4 inch apart in four rows of six. Cover with a clean kitchen towel and let rise for 45 minutes. The rolls will look puffy and will almost be touching, but most of the rising will take place during baking.

Step 6

About halfway into the rise, position a rack in the middle of the oven and preheat to 375 degrees.

Step 7

Bake for about 20 minutes, or until the rolls are touching and fill the pan; they will turn golden brown. Remove from the oven and brush with the melted butter. Using a spatula, slide the rolls onto a wire rack or serve directly from the pan, warm or at room temperature.