Preheat the oven to 350°F (175°C).
Bring a large pot of water to a boil, add a generous pinch of salt, then add the pasta and cook until barely al dente, about 8 minutes or about two-thirds of the package time. Drain and set aside.
Meanwhile, heat the olive oil in a large skillet over medium heat. Add the sliced mushrooms and sauté until softened, about 6–7 minutes.
Add the tomato-based pasta sauce to the skillet, bring to a boil, then reduce heat to low and simmer for about 15 minutes.
Assemble the casserole in an 8×8-inch baking dish: layer half the cooked pasta, then half the tomato sauce and mushrooms. Arrange the provolone slices over the sauce.
Dollop the sour cream in spoonfuls over the provolone and gently spread into a thin layer, then sprinkle the crumbled Gorgonzola over that layer.
Add the remaining pasta, top with the shredded mozzarella, then spread the remaining pasta sauce over the top and finish with the grated Parmesan.
Bake in the preheated oven for 30 minutes, or until the cheese is melted and bubbly. Let rest a few minutes before serving.