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Step 1
Preheat the oven to 350 degrees F (175 degrees C). Grease a 7x11-inch baking dish.
Step 2
Bring a large pot of lightly salted water to a boil; cook gemelli at a boil until flexible but still firm to the bite, about 6 minutes.
Step 3
Meanwhile, heat oil in a large skillet over medium heat until shimmering. Add onion and stir for 2 minutes. Add asparagus and mushrooms and continue to cook, stirring occasionally, until mushrooms begin to soften and asparagus is bright green, about 4 minutes.
Step 4
Add tomatoes, garlic, red pepper flakes, salt, and pepper. Continue cooking for about 4 minutes, stirring occasionally.
Step 5
Pour the vegetable mixture into a large mixing bowl. Drain pasta and stir into the bowl.
Step 6
Melt butter in the same skillet. Add flour and cook, stirring constantly, until the mixture bubbles, about 4 minutes. Pour in milk, stirring briskly to avoid lumps. Continue to stir until sauce thickens and bubbles again, about 4 minutes. Remove from heat and stir in 1/3 cup Parmigiano-Reggiano and provolone cheese until melted.
Step 7
Pour the cheese sauce over the pasta and vegetables and stir to combine. Pour into the prepared baking dish. Taste and adjust seasonings. Toss remaining Parmigiano-Reggiano with bread crumbs and sprinkle over the casserole.
Step 8
Bake in the preheated oven until bubbly and lightly browned, 20 to 25 minutes.