In a small bowl, combine the warm buttermilk, yeast, and 1 tablespoon of the sugar. Let it sit for 5 to 8 minutes until foamy. If it does not foam, start over with a fresh packet.

In a large bowl or stand mixer, combine the flour, remaining 2 tablespoons sugar, and salt. Add the yeast mixture, egg, and 4 tablespoons melted butter. Knead with a dough hook on low speed, or by hand on a floured surface, for 7 to 9 minutes until smooth and elastic.

Shape the dough into a ball and place it in a lightly greased bowl. Cover with plastic wrap and let it rise in a warm spot for 1 to 1 1/2 hours until doubled in size.

Grease a 9x13-inch baking dish. Punch down the risen dough and divide it into 16 equal pieces. Roll each piece into a smooth ball.

Place the dough balls in the prepared dish in 4 rows of 4. Cover loosely with plastic wrap and let them rise for 45 minutes to 1 hour until puffy.

Preheat the oven to 375°F. Brush the rolls with half of the remaining melted butter. Bake for 18 to 20 minutes until golden brown and hollow sounding when tapped. Brush with remaining melted butter after removing from the oven.