Sprinkle the yeast and sugar over 1 cup of warm water (90 to 100°) in the bowl of a stand mixer. Whisk to combine and then let sit until bubbles have formed on the top, about 5 minutes. Add the flour, 2 tablespoons of olive oil, and salt; mix with the dough hook on low speed until the dough comes together, about 2 minutes. Scrape the bottoms and sides of the bowl. Increase the speed to medium-low until everything is well incorporated, 2 to 3 minutes more.

Drizzle the top of the dough and down the sides of the bowl with 1 tablespoon of olive oil. Use a rubber spatula to flip the dough to coat in the oil. Cover the bowl with plastic wrap and let it rise for 1 hour. Continue onto step 3, or, if you want pizza another night, place the dough in the refrigerator for up to 2 days.

Pour 2 tablespoons of olive oil in a 12-inch cast-iron skillet. Use your hands to spread the oil around the bottom and sides of the skillet.

Transfer the dough to the prepared pan, flipping it to coat both sides in oil. Using your fingers, press the dough into the pan. If the dough keeps shrinking, cover the pan in plastic wrap and allow the dough to rest for 10 minutes before pressing it to cover the bottom of the pan. Cover the dough and allow it to proof for 1 ½ hours. Allow the dough to proof for an additional 30 minutes to 1 hour if the dough came from the refrigerator.

About 45 minutes before the dough is finished proofing, heat the oven to 475° and place one oven rack on the bottom of the oven.

Sprinkle the surface of the dough with 2 tablespoons of parmesan. Spread the Homemade Pizza Sauce evenly over the surface of the dough, reaching all the way to the edges. Sprinkle the dough evenly with 1 ½ cups of mozzarella cheese, all the way to the edges.

Remove the sausage from the casings and pinch off small pieces. Toss the peppers and onions with the remaining 1 tablespoon of olive oil. Top the pizza with the crumbled sausage, sweet peppers, red onion, and banana peppers. Sprinkle with the remaining ½ cup of mozzarella.

Bake the pizza on the bottom rack until the cheese is golden and bubbling and the bottom crust is deeply golden, 18 to 23 minutes.

Remove the pizza to a wire rack. Run an offset spatula or a butter knife around the edges of the crust to loosen the pizza and sprinkle with the parsley and the remaining 1 tablespoon parmesan. Allow the pizza to cool 5 minutes before carefully removing to a wire rack or a cutting board. Serve warm.