Preheat the oven to 375°F and generously butter a 24 cup mini muffin tin.

Stir the beaten egg and melted butter into the mashed potatoes until smooth and slightly glossy.

Press about 1 tablespoon of the potato mixture into each muffin cup, pushing it up the sides to form a shell with a well in the middle.

In a skillet over medium heat, brown the ground beef with the onion and carrot for 6 to 8 minutes, breaking up the meat, until no pink remains.

Stir in the tomato paste, beef broth, Worcestershire, salt, and pepper, and simmer for 5 minutes, until the liquid thickens enough to coat the back of a spoon.

Stir in the frozen peas and remove the skillet from heat.

Spoon the filling into the potato shells, filling each almost to the top.

Sprinkle the cheddar over the tops and bake for 18 to 20 minutes, until the potato edges turn golden brown and the cheese fully melts.

Let the bites cool in the pan for 5 minutes before running a thin knife around each one and lifting it out.