Combine water, sugar, and yeast in the bowl of a stand mixer. Let sit for 5 minutes to let the yeast bloom.
Add salt and oil to the yeast mixture. Turn mixer on to medium speed and slowly add flour. Beat for three minutes until the dough has formed a cohesive ball and does not stick to the bowl.
Remove the dough from the mixer bowl and spray the bowl with non-stick spray. Replace the dough ball and cover the bowl with plastic wrap. Let the dough rise in a draft-free environment for 3 hours, or until doubled in size.
Preheat oven to 375° Fahrenheit.
Roll the dough into a long rectangle on a lightly floured surface. Evenly sprinkle the top of the dough with mozzarella cheese. Top with pepperoni.
Roll the dough lengthwise and pinch the seams to seal the dough. Slice the dough into 1 ½" thick slices.
Place the slices on a baking sheet that has been lightly sprayed with non-stick spray or covered with Silpat or parchment paper. Sprinkle pinwheels with Parmesan cheese and basil.
Bake for 20-25 minutes or until golden brown.
Video
Notes
To speed up the rising time, lower your oven rack and turn on the oven and let it reach 150 degrees. Turn the oven off and place the dough in the oven. Check the dough after 45 minutes have passed.