Saute shallots and garlic in 1/4 cup plus 2 tablespoons margarine in a saucepan over medium-high heat until tender. Add flour, stirring until smooth. Cook 1 minute over medium heat, stirring constantly. Gradually add half-and-half and chicken broth; cook over medium heat, stirring constantly, until mixture is thickened and bubbly. Remove from heat; add Gruyère cheese, salt, and pepper, stirring until cheese melts.
Spread 1/2 cup cheese sauce in a greased 11- x 7- x 1 1/2-inch baking dish. Add broccoli and 1 1/2 cups cheese sauce. Top with chicken and remaining cheese sauce.
Combine Parmesan cheese, breadcrumbs, paprika, and remaining 2 tablespoons margarine; stir well. Sprinkle evenly over top of casserole. Bake, uncovered, at 350° for 30 minutes or until thoroughly heated.