Preheat oven to 425 degrees F.
Bring water to a boil in a large pot and add 2 Tbsp salt. Cook pasta 2 minutes fewer than the package directs. It should be too firm to eat.
Drain and rinse under cold water until cool. Drain and put in a large bowl.
Meanwhile, warm olive oil in a large skillet over high heat until smoking. Add onion and cook until light golden brown (5 minutes).
Add mushrooms and cook until they have given off their water and it has evaporated (8 to 10 minutes).
Add wine, spaghetti sauce, butter and salt and pepper to taste. Reduce heat to medium and cook until thickened (5 minutes).
Add mushroom mixture to bowl with the pasta. Add mozzarella and mix together. Transfer pasta to a baking dish and top with grated Parmigano-Reggiano.
Bake until bubbling and crusty on top (20 minutes).