Chicken Marsala with Portobello Mushrooms

Name: Chicken Marsala with Portobello Mushrooms
Ingredients: 8 tablespoons butter, divided; 2 tablespoons olive oil, divided; 4 portobello mushroom caps, sliced; 1 clove garlic, chopped; 1 tablespoon all-purpose flour; 1 (14.5 ounce) can beef broth; 0.5 cup dry Marsala wine; 1 tablespoon browning sauce; kosher salt, or to taste; 0.25 teaspoon ground black pepper, or to taste; 6 skinless, boneless chicken breast halves - pounded to 1/2 inch thickness; 1 pinch kosher salt and pepper to taste; 0.75 cup all-purpose flour, or as needed