Preheat your oven to 375°F. Prepare a 9×13-inch baking dish by coating it with nonstick cooking spray.

Season the chicken cutlets on both sides with salt and pepper. Set aside 3 tablespoons of the flour, then dredge the chicken in the remaining flour to coat evenly.

Heat 3 tablespoons of butter in a skillet over medium-high heat. Add the floured chicken cutlets to the skillet, cooking each side for 3-4 minutes until lightly browned. Do not fully cook the chicken. Transfer the seared cutlets to the prepared baking dish.

In the same skillet, melt the remaining 3 tablespoons of butter. Sauté the minced onion and diced mushrooms in the butter, stirring frequently, until softened and aromatic, approximately 4-5 minutes.

Add the minced garlic to the skillet and sauté for 1 minute until fragrant. Sprinkle the reserved 3 tablespoons of flour into the skillet, stirring to form a roux-like paste.

Gradually whisk in the heavy cream, chicken broth, and red wine vinegar, combining thoroughly. Adjust seasoning with additional salt and pepper to taste.

Pour the prepared sauce over the chicken in the baking dish. Lay a slice of Muenster cheese over each cutlet, ensuring full coverage. Cover the dish with aluminum foil and bake for 20 minutes.

Remove the foil, switch the oven to broil, and broil the dish for 2-3 minutes, or until the cheese becomes bubbly and slightly golden.

Allow the dish to rest for a few minutes before serving. Enjoy your Chicken Gloria!