Heat 1 tablespoon oil in a large sauté pan over medium heat; add sausage. Sauté, breaking up meat until no longer pink and beginning to brown. Transfer to a plate with a slotted spoon; pour off drippings, leaving behind brown bits. Add remaining oil and mushrooms to pan. Sauté until mushrooms begin to brown, 6 to 8 minutes. Add shallots; sauté 3 minutes. Stir in garlic and rosemary; sauté 1 minute more. Add wine, increase heat to medium-high, and cook until wine is nearly evaporated. Season with ¾ teaspoon salt and pepper. Return sausage to pan and stir to combine.
Preheat oven to 375F. Lightly oil a 13 x 9-inch baking dish.
Melt butter in a large saucepan over medium heat. Stir in flour; cook until foaming but not colored, about 2 minutes. Whisk in milk; bring to a simmer. Cook until thickened, about 5 minutes. Season with remaining ¼ teaspoon salt.
Cook rigatoni according to package directions, undercooking it by 3 minutes. Drain; return to pot. Add sausage mixture to pasta; toss well. Add béchamel and crushed tomatoes; stir to combine. Stir in fontina and 2 tablespoons Parmigiano Reggiano.
Transfer pasta mixture to baking dish. Sprinkle remaining Parmigiano Reggiano over top; cover with foil. Bake 20 minutes. Remove foil and bake 10 minutes more. Let stand 5 minutes before serving.