Preheat the oven to 425˚F.
Mold the biscuits into the shape of each muffin cup. Bake in the preheated oven for 6-8 minutes, or until lightly brown. Remove from oven, and set aside.
Meanwhile, heat the oil on a medium skillet over medium heat. Add the ground beef, and cook until brown. Add in the onions, garlic, carrots and peas until the onions are transparent and fragrant, around 2-3 minutes. Remove from heat, and mix in the ketchup, salt and pepper.
Microwave the leftover mashed potatoes until warm, around 2-3 minutes.
Scoop equal amounts of the ground beef mixture into each muffin cup. Top each with mashed potatoes, and sprinkle the grated cheese on top.
Return to the oven, and bake for around 12-15 minutes, or until the cheese is melted.