In the bowl of a stand mixer with a dough hook attachment, combine water, 1 teaspoon sugar, and yeast. Allow it to sit for about 5 minutes until sugar and yeast dissolve.
Add remaining sugar, warm milk, 6 tablespoons melted butter, and salt. Mix until combined.
Add the egg and mix to combine.
Incorporate the flour into the yeast mixture, mixing for about 3 minutes at medium-high speed. Scrape the dough into the center of the bowl.
Knead the dough on low speed for 3-4 minutes, or until it forms a smooth and elastic ball. The dough is ready when it no longer sticks to the sides of the bowl.
Place the dough in a large bowl that is lightly sprayed with cooking spray, cover, and let the dough rise in a warm place for 1-2 hours or until doubled in size.
Preheat the oven to 350°F. Lightly spray a 9×13-inch baking dish with cooking spray.
Gently punch down the risen dough, divide it into 12 equal pieces, and shape each into a smooth ball. Place in the prepared baking dish.
Cover the rolls and let them rise for about 30 minutes, or until doubled.
Bake for 12-15 minutes or until golden brown. Brush with the remaining tablespoon of melted butter.