Stir 1 tablespoon of the sugar into warm water (95°F to 110°F or 35°C to 43°C) and stir in the yeast until dissolved. Set aside to let it foam up.
Combine in the bowl of a stand mixer, the flour, salt, and remainder of the granulated sugar. Equip the mixer with a dough hook and stir to combine.
Add the melted butter, milk, egg, and proofed yeast mixture into the dry ingredients. Stir the wet and dry ingredients on low until combined.
Increase the speed of the mixer to medium in order for the dough to knead and comes together in a ball. Notice that the dough should be stretchy, and tacky, not sticky.
Shape the dough into a large bowl and place it on a lightly floured surface. Cover with plastic wrap and let it rest for 15 minutes.
Divide the dough into 16 equal pieces. Use a kitchen scale to weigh the total weight of the dough and then divide accordingly.
Shape each piece of dough into a ball with your finger. Stretch out the piece to create a smooth surface and bunch up the dough underneath, pinching it closed.
Place the balls of dough into a lightly greased 9"x13" baking dish, creating 4 rows of 4, spacing them evenly. Cover the baking dish in plastic wrap and let them rise for 40 minutes or until they have doubled in size.
Notice that the dinner rolls are ready to bake when they they have filled up the surface of the baking dish. Sprinkle the top of the buns with flour, using a small mesh sifter.
Place in a preheated 380F oven. Bake for 25 minutes, or until the tops and side are lightly golden in color.
Remove from the oven and let them cool for 5-10 minutes. Carefully remove them from the pan and place on a cooling rack, to prevent the buns from "sweating" and making sure the crust can crisp up.