Mix cooled mashed potatoes with egg, flour, cornstarch, melted butter, and seasonings until a soft dough forms. Let rest for 5–10 minutes.
Sauté onion and garlic in olive oil, then add ground beef. Cook until browned and season with paprika, thyme, salt, and pepper. Stir in tomato paste and a bit of cheese if desired, then let cool.
Flatten portions of dough, fill with meat mixture, seal, and shape into patties.
Fry in oil or butter for 3–4 minutes per side until golden and crisp.
Serve warm with sour cream, spicy mayo, or ranch, topped with herbs or grated cheese.