Chicago-Style Deep Dish Pizza

4 tablespoons extra-virgin olive oil 1 pound sweet or hot Italian sausage, sliced into thin rounds (about 8 links) 2 tablespoons unsalted butter, softened 1 pound fresh pizza dough, at room temperature 10 ounces whole milk low-moisture mozzarella, thinly sliced 1 cup your favorite marinara sauce or 1 1/2 cups crushed and strained San Marzano tomatoes 3 cloves garlic, minced 1 tablespoon dried oregano 1/2 cup grated Parmesan