Steam broccoli until tender, 3 to 4 minutes. Rinse and coarsley chop.

Heat olive oil in saucepan over medium heat. Add onion, thyme, salt, and pepper. Cook until tender, about 5 minutes. Add wine, increase heat to high and cook until evaporated, about 3 minutes. Remove from heat. Stir in alfredo sauce, 1/2 cup cheese, milk, and nutmeg. Then stir in pasta, broccoli, and chicken.

Transfer to 9 by 13 baking dish. Top with remaining cheese and breadcrumbs. Sprinkle with paprika, cover with foil and bake at 375 degrees for 30 minutes. Uncover and bake 15 minutes more. Can be made 1 day in advance and refrigerated or frozen. If frozen, thaw in refrigerator and bake as directed.