Preheat oven to 350 degrees. Lightly grease a 2-quart baking dish.
In a large skillet over medium heat, sauté onion in olive oil until lightly browned. Add beef and butter and sauté for about 1 minute longer. Stir in the flour until blended. Add beef broth, Worcestershire sauce, and peas and carrots. Season with salt and pepper. Cook until heated through and slightly thickened. Spoon mixture into prepared baking dish.
If using leftover mashed potatoes, warm them in a saucepan with a little butter or milk until softened. Stir sour cream and cheese into the potatoes. Spoon potatoes evenly over the beef layer and sprinkle lightly with paprika.
Bake for 25 to 35 minutes, until hot and bubbly. If desired, turn on the broiler to brown the top for just a minute or two, watch carefully to prevent burning.