In the bowl of a stand mixer fitted with the dough hook, combine the water and yeast and stir to combine. Wait 5 minutes, until the yeast is a little foamy. Add the olive oil and flour and mix on low. As the dough comes together, add the salt.
Mix the dough on medium-low speed until smooth and elastic, about 8 to 10 minutes. Transfer to a greased bowl, cover with plastic wrap, and let it rise for about 2 hours at room temperature.
Heat the olive oil and butter in a skillet over medium heat and add the onions and garlic. Cook for 2 to 3 minutes until softened and fragrant. Add the red pepper flakes, tomato paste, and whole tomatoes.
Use a wooden spoon to break the tomatoes up and simmer for 5 to 10 minutes until most of the liquid has evaporated. Add the vodka and simmer for 3 to 4 minutes. Season with salt and pepper and add the heavy cream. Transfer the mixture to a blender and puree until smooth. Set aside.
Preheat an oven to 450 F. Drizzle a nonstick 9 × 13-inch baking pan with the olive oil.
Scrape the proofed pizza dough into the prepared baking pan and toss to coat in the olive oil. Use your fingers to gently stretch the pizza to the edges of the pan. If it springs back, wait 5 minutes, and stretch some more until the dough reaches the edges. Cover the pan with a damp kitchen towel and let the dough rise for 45 minutes, until puffy.
Spread sauce all over the surface of the dough. Top with the grated provolone, then evenly distribute the torn mozzarella all over. Top with pepperoni and dot with more sauce. Bake for 22 to 25 minutes, until the pepperoni is crispy and the cheese is browned. Cool for 5 minutes before serving.