In the bowl of a stand mixer, combine warm milk, 1 tablespoon of the sugar, and the yeast. Let sit for 5-10 minutes until foamy and activated.

Add the remaining sugar, melted butter, eggs, and salt to the yeast mixture. Mix using the paddle attachment until well combined.

Gradually add 4 cups of flour, one cup at a time, mixing on low speed. Once all the flour is incorporated, switch to the dough hook attachment.

Knead the dough on medium-low speed for 7-8 minutes until smooth and elastic. If the dough is still very sticky after 4 cups of flour, add the remaining 1/2 cup a little at a time until the dough pulls away from the sides of the bowl but is still tacky to the touch.

Transfer the dough to a lightly oiled bowl, turning once to coat. Cover with plastic wrap or a clean kitchen towel and let rise in a warm place until doubled in size, about 1-1.5 hours.

Punch down the dough and turn out onto a lightly floured surface. Divide the dough into 15 equal pieces (about a tablespoon-sized).

Shape each piece into a smooth ball by pulling the edges toward the center and pinching to seal. Place the ball seam-side down and cup your hand around it, gently rolling in a circular motion to create surface tension and a perfectly round shape.

Arrange the shaped rolls in a greased 9×13-inch baking pan, spacing them evenly. Cover and let rise again until puffy and nearly doubled, about 45-60 minutes.

Preheat oven to 375°F.

Before baking, gently brush the tops of the rolls with some of the very soft butter.

Bake for 15-20 minutes, until golden brown on top and baked through. An instant-read thermometer inserted into the center of a roll should read about 190°F.

While still hot from the oven, brush the tops generously with more soft butter, allowing it to melt into the warm rolls. If desired, sprinkle with flaky sea salt or drizzle with honey.

Allow to cool for 10 minutes in the pan before serving warm.