Saute shallots and garlic in 1 tablespoon margarine in a saucepan over medium-high heat until tender. Combine flour and 1/2 cup chicken broth; stir well. Add flour mixture and remaining 1 cup chicken broth to saucepan. Cook over medium heat, stirring constantly, until mixture is thickened. Remove from heat; add sour cream and next 4 ingredients.
Spread 1/2 cup sour cream mixture in an 11- x 7- x 1 1/2-inch baking dish coated with cooking spray. Add broccoli and 1 1/4 cups sour cream mixture. Top with chicken and remaining sour cream mixture.
Combine breadcrumbs, 2 tablespoons Parmesan cheese, parsley, and remaining 1 tablespoon margarine; stir well. Sprinkle evenly over top of casserole. Bake, uncovered, at 350° for 30 minutes or until thoroughly heated.