Heat a skillet over medium-high heat with olive oil. Add ground beef and cook until fully browned. Season with salt and pepper, then set aside.
In the same skillet, sauté onions and carrots for about 5 minutes until soft and golden.
Return the meat to the pan, add garlic and parsley, and cook for 1 minute. Remove from heat.
In a bowl, mix mashed potatoes with egg and flour until combined.
Take a scoop of potato mixture, flatten into a disk, and place filling in the center. Seal edges and shape into a pancake.
Coat each pancake in breadcrumbs and gently flatten.
Heat oil in a pan and cook pancakes for 3–4 minutes per side until golden brown.
Serve warm and enjoy your Mashed Potato Pancakes with Meat Filling.