Gather all ingredients. Preheat the oven to 350 degrees F (175 degrees C). Grease a 2-quart casserole dish with cooking spray. Heat oil in a large skillet over medium heat. Cook and stir the onion in hot oil until translucent, about 5 minutes. Add ground beef and basil. Cook and stir until beef is crumbly and browned, about 5 minutes. Mix in green beans, tomatoes, and garlic; cook until beans are slightly softened, about 5 minutes more. Transfer to the prepared casserole dish. Mix mashed potatoes, water, and beaten egg in a medium bowl until smooth. Spread evenly over the beef mixture. Bake in the preheated oven until potatoes start to brown on top, 15 to 20 minutes. Sprinkle with cheese and continue baking until cheese is melted, about 5 more minutes. Serve and enjoy! Yields one casserole.