Start by pounding the chicken breasts to an even thickness. This helps them cook evenly and stay juicy. Season both sides with salt and black pepper.
In a shallow dish, combine the all-purpose flour with a teaspoon of salt and black pepper. Dredge each chicken breast in the flour mixture, shaking off any excess.
In a large skillet, heat the olive oil and butter over medium heat. Once hot, add the chicken breasts and sear for about 5-6 minutes on each side until they are golden brown and cooked through. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and sauté until translucent. Add the sliced mushrooms and cook until they are browned. Stir in the minced garlic and dried thyme, cooking for an additional minute until fragrant.
Pour in the chicken broth and whole milk, stirring to combine. In a small bowl, mix the cornstarch with a tablespoon of water to create a slurry. Add this to the skillet, stirring until the sauce thickens.
Return the chicken to the skillet, nestling it into the sauce. Cover the chicken with slices of Muenster cheese, allowing it to melt into the sauce.
Serve the Chicken Gloria hot, spooning the creamy sauce over the chicken. It pairs beautifully with rice, pasta, or a simple green salad.