2. Melt 1/2 cup butter and heat 1 tablespoon vegetable oil in a skillet over medium heat. Cook and stir the mushroom slices in the skillet until tender. Remove from heat, cover to keep warm, and set aside.
3. Melt the remaining butter and heat the remaining oil in a saucepan over medium-high heat. Cook and stir the garlic until tender, then gradually whisk in the flour. Increase heat to high, and pour in the beef broth and Marsala wine. Season with kosher salt and pepper, and whisk in the browning sauce. Bring to a boil, and reduce heat to low. Mix in the mushrooms, reserving remaining butter and oil in the skillet. Cover saucepan, remove from heat, and set aside.
4. Season chicken with salt and pepper, and dredge in the remaining flour. Over medium heat, reheat the remaining butter and oil in the skillet used to cook the mushrooms. Cook the chicken 2 minutes per side, until browned. Arrange the chicken in the bottom of a 9x13 inch baking dish, and cover with the sauce and mushroom mixture.
5. Cover baking dish, and bake 25 minutes in the preheated oven, or until chicken juices run clear.