Preheat the oven to 350°F.
Season chicken with salt and pepper, then use 5 tablespoons of flour to dredge chicken, shaking off excess.
In a skillet over medium-high heat, heat olive oil and 2 tablespoons butter. Add chicken and brown on both sides, about 3-4 minutes per side. Transfer to a 9x13-inch baking dish.
In the same skillet, add onions and garlic. Sauté until onions are translucent. Add mushrooms and sprinkle on remaining 3 tablespoons of flour. Cook until golden.
Deglaze with sherry, then add chicken broth and bring to a simmer. Stir in half-and-half, and simmer until slightly thickened.
Pour the mushroom sauce over the chicken in the baking dish. Top with slices of Muenster cheese. Cover with foil and bake for 25 minutes. Remove foil, then broil for 3-5 minutes until cheese is bubbly and golden.