Activate the yeast. 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 2 to 3 minutes until it is foamy.
Feed the yeast with some flour. Stir one cup of the flour into the yeast mixture. Set this aside.
Add the remaining ingredients to an electric mixer. 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.
Add yeast mix and more flour, if needed. Process until the dough comes together. Add the rest of the yeast mixture. Add 1/4 cup of flour until the dough comes away from the sides of the bowl. You may have some flour left over.
First rise. Put the dough in a bowl coated with cooking spray. Cover the bowl with plastic wrap and let the dough rise and double for about 2 hours.
Prep the garlic butter. While the dough is rising, make the garlic butter. Mix together the butter, garlic, and parsley, and season with salt and pepper.
Roll out and slather. Roll the dough out into a rectangle about 16 inches by 10 inches. Mine is not very pretty, you will take your time, won't you? Slather the dough with garlic butter.
Cut. I used a pizza cutter to cut the dough into strips.
Shape. Roll the strips up and put them in the pan on their sides.
Second rise. Cover the pan with a towel and let rise for about 45 minutes.
Spinkle the Parmesan. Once risen, sprinkle with grated Parmesan cheese.
Bake! Bake the garlic rolls in a preheated 375-degree oven for 15 to 20 minutes, or until golden brown.