In a small bowl, combine the warm milk, one tablespoon of sugar, and the yeast. Let it sit for about 10 minutes until it becomes frothy and active.

In the bowl of a stand mixer fitted with a dough hook, combine the flour, remaining sugar, and salt. Pour in the yeast mixture and the two eggs. Mix on low speed until a shaggy dough forms.

Increase the speed to medium and begin adding the softened butter one cube at a time. Wait until each piece is fully incorporated before adding the next. This process ensures the milk brioche rolls develop a rich, elastic crumb.

Knead the dough for about 10–12 minutes until it is smooth, glossy, and pulls away from the sides of the bowl. Place the dough in a lightly greased bowl, cover with a damp cloth, and let it rise in a warm spot for 1.5 to 2 hours, or until doubled in size.

Gently deflate the dough and divide it into 12 to 15 equal portions. Roll each portion into a smooth ball and place them in a parchment-lined baking pan, leaving a small gap between each roll.

Cover the rolls and let them rise again for 45–60 minutes. Meanwhile, preheat your oven to 350°F (175°C).

Brush the tops with a beaten egg mixed with a splash of milk. Bake for 22–25 minutes until the milk brioche rolls are a deep golden brown. Brush with melted butter immediately after removing them from the oven for a professional finish.