Combine the chilled mashed potatoes in a mixing bowl with chopped dill, minced garlic, salt, pepper, and the egg. Mix until well incorporated and the mixture holds together, adding flour gradually to help it form a dough-like consistency.
Divide the mixture into four equal portions and gently shape each into a round patty, about 1/2 inch thick. Press lightly to create even discs.
Heat a skillet over medium heat and add a tablespoon of oil. Once shimmering, carefully place the patties into the hot oil, spacing them apart for even browning.
Cook the patties for about 4-5 minutes per side, until they develop a crispy, golden-brown crust and are heated through. Adjust heat as needed to avoid burning.
Use a spatula to carefully flip the patties and cook the other side until similarly golden and crispy. You should hear a satisfying sizzle as they fry.
Once cooked, transfer the patties to a plate or cooling rack. Let them rest for a minute to settle and fully crisp up.
Serve the crispy mash potato patties hot, garnished with additional dill if desired. Enjoy their tender interior paired with their crunchy exterior.
