Mix together the yeast and water. Measure 1/3 cup of sugar and add 2 Tablespoons from the measured sugar to the bowl. Whisk these together until the yeast is dissolved. Let the yeast stand for about 10 minutes.
Stir one cup of the flour into the yeast mixture. Set this aside.
In the bowl of a stand mixer or in the food processor, add 2 cups of flour, the rest of the sugar, melted butter, milk, and salt.
Process until the dough comes together. Add 1/4 cup of flour until the dough comes away from the sides of the bowl. You may have some flour left over.
Put the dough in a bowl coated with cooking spray. Cover the bowl with plastic wrap and let the dough rise and double about 2 hours.
While the dough is rising, make the garlic butter. Mix together the butter, garlic, parsley, and season with salt and pepper.
Roll the dough out into a rectangle about 16 inches by 10 inches. Spread the dough with the garlic butter.
I used a pizza cutter to cut the dough into strips.
Roll the strips up and put them in the pan on their sides.
Cover the pan with a towel and let rise for about 45 minutes.
Once risen, sprinkle with grated Parmesan cheese.
Bake the garlic rolls in a preheated 375-degree oven for 15 to 20 minutes or until golden brown.