1. Bring a large pot of water to a boil. Add broccoli and blanch 3 minutes. Drain and rinse with cold water to stop cooking.
2. Preheat oven to 350°F. Mist a 9-by-13-inch baking dish with cooking spray.
3. Season chicken with salt and pepper. Mist a large skillet or grill pan with cooking spray; place over medium-low heat. Cook chicken, turning once, until browned and almost cooked through, about 10 minutes. Remove from heat; transfer chicken to a cutting board. When cool, slice chicken into bite-size pieces.
4. Warm a medium skillet over medium heat. Add butter and 2 tsp. oil; heat until butter has melted. Add garlic and shallots and sauté until tender, about 3 minutes. Sprinkle flour over mixture and whisk until incorporated. Stir in broth, milk and sherry and bring to a boil. Remove from heat and stir in half of Swiss cheese. Season with salt and pepper.
5. Arrange broccoli in baking dish and pour half of sauce on top. Arrange chicken on top and cover with remaining sauce. Sprinkle with remaining Swiss cheese and Parmesan; top with bread crumbs. Drizzle with 1/2 tsp. olive oil.
6. Bake for 30 minutes or until browned on top; serve hot.
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