Heat the oven to 400°F. Lightly grease 8 cups of a standard muffin tin.

In a large bowl, combine the egg, breadcrumbs, milk, onion, Worcestershire sauce, salt, and pepper. Add the ground beef and mix gently until just combined.

Divide the meat mixture into 8 portions. Press half of each portion into the bottom of a prepared muffin cup, leaving a small dip in the center. Place a cheddar cube in each dip, then cover with the remaining meat mixture and pinch the edges closed. Spread the ketchup over the tops.

Toss the halved potatoes with the olive oil. Arrange them in a single layer on a rimmed baking sheet, cut sides down, and place the sheet in the oven.

After the potatoes have roasted for 15 minutes, add the broccoli to the baking sheet and stir to coat it with the oil already on the pan. Put the muffin tin in the oven alongside the vegetables.

Bake until the meatloaf muffins are cooked through and the potatoes are tender, about 20 to 25 minutes. The broccoli should be tender with lightly browned edges. Check that the centers of the muffins reach 160°F. Rest them for 5 minutes before removing from the tin, then serve with the potatoes and broccoli.