1. Preheat oven to 350°.
2. Combine flour and butter; stir well. Heat a large nonstick skillet over medium-high heat. Coat pan with cooking spray. Add onion and carrot; sauté 5 minutes. Add mushrooms; sauté for 5 minutes or until lightly browned. Remove vegetables from skillet. Add beef to pan; cook 5 minutes or until browned, stirring to crumble. Stir in tomato paste, and cook 3 minutes. Stir in broth and pepper. Return vegetables to pan, and bring to a simmer. Stir in parsley, thyme, and salt. Add flour mixture, and cook for 1 minute or until thick, stirring constantly.
3. Spoon meat mixture into an 8-inch square glass or ceramic baking dish coated with cooking spray, spreading evenly. Combine the potatoes and half of cheese; spread the potato mixture evenly over meat mixture. Top with remaining cheese. Sprinkle with paprika, if desired. Bake at 350° for 20 minutes or until bubbly.