Preheat the oven to 350°F and lightly grease a standard 12-cup muffin pan.
Add the ground beef, grated onion, carrots, panko, eggs, ketchup, Parmesan, garlic powder, oregano, thyme, baking soda, salt, and pepper to a large bowl. Gently mix everything together just until combined.
Divide the mixture evenly between the 12 muffin cups. Gently press it into each cup without packing the meat too tightly.
Bake for about 15–25 minutes, or until the meatloaf muffins are cooked through and reach 160°F (71°C) in the center.
While they bake, peel and chop the potatoes. Boil or steam until tender, then drain well. Add the butter and 1/2 cup milk and mash until smooth, adding more milk as needed. Keep the mashed potatoes creamy but thick enough to hold their shape on top.
Let the muffins rest for a few minutes, then carefully remove them from the pan and transfer them to a serving platter before adding the ketchup and mashed potatoes.
Add a little ketchup to each meatloaf muffin, then spoon or pipe the mashed potatoes on top.
Sprinkle with parsley if you want and serve warm.