In a small bowl stir together the sugar and yeast. Pour into the bottom of the bowl of a stand mixer. Pour the water over it and let it sit for 5 minutes. It will be frothy and bubbly.
Add softened butter, salt, and 3 cups of flour. Mix on medium low speed, using the dough hook, until combined. Add additional flour, 1/4 cup at a time, until dough pulls away from the sides of the bowl. The dough should still be slightly sticky and soft. Be sure to not add too much flour.
Knead for 5 minutes (I just used the dough hook to knead it in the stand mixer bowl) until it looks smooth. Cover with a towel and let rise for 20 minutes.
Prepare a 9 x13 baking dish by spraying with cooking spray or lining with parchment paper.
Gently punch down the dough and divide into 20 pieces (each piece will be a bit larger than a golf ball). Roll each piece into a ball and place into the prepared baking dish.
Brush rolls with the melted butter (I save some of this to brush on the rolls after they cook) and sprinkle with sea salt. Let rise, uncovered, for 15 minutes.
While rolls are rising heat oven to 400 degrees.
Cook rolls for 15-18 minutes or until tops are golden brown. Serve warm!