Cheesy Baked Pasta with Vegetables

Heat oven to 425 ºF. Butter a shallow 3-qt baking dish. Cook the pasta according to package directions, adding the broccoli during the last 3 minutes of cooking; drain and return the broccoli and pasta to the pot. Meanwhile, melt the butter in a large deep skillet over medium heat. Add shallots and mushrooms and sauté until tender, 5 minutes. In a medium bowl, whisk together milk, flour, salt and pepper. Pour into skillet and bring to a boil. Reduce heat and simmer, stirring occasionally, until thickened, about 5 minutes; stir in spinach. Remove from heat and stir in 1 cup of the fontina and 1 ⁄3 cup of the Parmesan. Pour sauce into pot with pasta and broccoli and toss to coat. Transfer to the prepared baking dish and sprinkle with remaining fontina and Parmesan. Bake until the cheese melts and is beginning to brown, about 10 minutes. After completing step 5, let casserole cool for 10 minutes. Cover with plastic wrap and refrigerate for up to 3 days. On the night you'd like to serve it, remove casserole from refrigerator and replace plastic wrap with nonstick aluminum foil. Bake in a 425 °F oven for 30 minutes; uncover and bake until beginning to brown, 10 minutes.