Season Chicken breasts with Salt and Black pepper.
Heat Olive oil in a large skillet over medium-high heat. Sear Chicken breasts for 5-7 minutes per side, or until cooked through. Remove from skillet and set aside.
In the same skillet, melt Butter over medium heat. Add Sliced mushrooms and Garlic and cook until softened, about 5-7 minutes.
Sprinkle Flour over the mushrooms and cook for 1 minute, stirring constantly.
Gradually whisk in Chicken broth and Worcestershire sauce. Bring to a simmer and cook until Sauce has thickened, about 2-3 minutes. Stir in Dried thyme.
Return Chicken breasts to the skillet. Spoon Sauce over the Chicken and top with shredded Monterey Jack cheese.
Cover the skillet and cook until Cheese is melted, about 2-3 minutes. Serve immediately.
