Saute beef, onion, celery, and garlic in a large pan in butter until well done. Strain off fat. Boil potatoes until fork tender, about 20 minutes. Drain and mash with butter. Blanch carrots and add to beef mixture. Make a gravy with beef base and water. Whisk in enough flour to thicken, about 2 tablespoons. When gravy comes to a boil, add beef=carrot mixture, reduce heat and simmer for 5 minutes. Spoon meat mixture into a 2-quart casserole. Spoon potatoes on top. Bake for 20 minutes at 350 degrees. Top with cheese and let sit until cheese melts from the radiated heat. about 5 minutes.