Butterfly the chicken breast lengthways to create 2 thin breast pieces. Season the chicken on both sides with salt and pepper. Dip in flour, shaking off excess.
Heat oil in a nonstick pan over medium-high heat. Cook chicken for 2-3 minutes per side, until the outside is golden brown. Set aside on a paper towel lined dish.
Add shallots and mushrooms to pan. Sauté until mushrooms are soft and beginning to brown, about 5 minutes.
Stir 2 tablespoons of flour into the mushrooms and cook for 1 minute. Add beef broth and cook for an additional 1-2 minutes, scraping any brown bits from the bottom of the pan to incorporate into the sauce. Simmer for 5-8 minutes, until sauce is slightly thickened.
Add chicken back into the pan, stir in thyme and butter and simmer for 6 -8 minutes. Place the cheese on top and melt. You want the sauce to be a smooth thick consistency. If the sauce is too thick add a little more broth to thin it out. Season with salt and pepper to taste before serving.