In a small, heat-resistant bowl, combine the yeast with 1 tablespoon of sugar. Set aside.

In a small saucepan, heat the milk and butter over medium-low heat until the mixture reaches 110°F (about 5-6 minutes). Do not let it boil. It’s fine if all the butter doesn’t fully melt. Remove from heat.

Pour ¼ cup of the warm milk mixture into the yeast mixture and whisk gently. Let it sit for 10 minutes until foamy and doubled in size. If it doesn’t foam, your yeast is inactive—replace it and repeat steps 1-3.

In the bowl of a stand mixer fitted with the dough hook, whisk together the eggs, egg yolk, and ½ cup of sugar.

Gradually add the remaining milk mixture (from step 2) to the egg mixture and whisk until smooth and combined.

Add 3 cups of flour and the salt to the wet mixture. Turn on the mixer to low speed and mix for 30 seconds, or until a soft, limp dough begins to form.

Add the prepared yeast mixture and 1½ more cups of flour. Mix on low speed until most of the flour is incorporated (about 90 seconds). If the dough feels too sticky, add up to ½ cup additional flour, ¼ cup at a time, until the dough is soft but manageable.

Increase the mixer speed to medium (speed 6) and knead the dough for 7-8 minutes. The dough should become smooth, slightly shiny, and elastic.

Perform the "windowpane test" by stretching a small piece of dough. It should stretch thin enough to see through without tearing. If it tears, knead for 1-2 more minutes at low speed.

Lightly flour your hands and countertop. Transfer the dough to the counter and gently knead it 4-5 times.

Place the dough in a lightly greased bowl, turning it once to coat all sides. Cover with a clean kitchen towel and let it rise in a warm spot for 1 hour, or until doubled in size.

Spray a 9x13-inch pan with nonstick baking spray, coating the bottom and sides.

After the first rise, gently deflate the dough by pulling it away from the sides of the bowl and folding it toward the center. Repeat on all sides until the dough forms a loose ball.

Transfer the dough to a lightly floured surface. Stretch it into a 24-inch-long log and divide it evenly into 24 pieces (each about 2 ounces). Use a kitchen scale for accuracy if needed.

Take one piece of dough and gather the edges to the center, pinching them together at the bottom to form a smooth top.

Lightly flour your hands, then roll the dough on the counter with the pinched side down to create a taut, round ball.

Place the dough ball in the prepared pan. Repeat with the remaining pieces, arranging them in 6 rows of 4. Cover unused dough pieces with a kitchen towel to prevent drying out.

Cover the pan with a clean kitchen towel and let the rolls rise in a warm spot for about 1 hour to 1 hour 15 minutes, or until doubled in size.

About 10 minutes before the rolls finish rising, preheat the oven to 375°F. Place the oven rack in the middle position.

Gently brush the tops of the rolls with the reserved egg white.

Bake in the preheated oven for 20-24 minutes, or until golden brown and a digital thermometer inserted into the center of a roll reads 190°F. Begin checking at the 20-minute mark to avoid over-browning.

Remove the rolls from the oven and let them cool in the pan for 10 minutes.

Brush the tops with melted butter for a soft, glossy finish.

Serve warm, and enjoy the fluffy, buttery rolls!