Season chicken breasts with salt and pepper, then dredge lightly in flour.
Heat olive oil and 2 tablespoons butter in a skillet over medium heat.
Brown chicken on both sides until golden, then remove from pan.
In the same pan, sauté mushrooms and garlic in remaining butter until soft.
Sprinkle 2 tablespoons flour over mushrooms; cook for 1 minute while stirring.
Slowly add sherry and cream, stirring until sauce thickens.
Return chicken to pan; top each piece with Muenster cheese slices.
Cover and cook until cheese melts and chicken is cooked through, about 5 minutes.