Heat the oven to 400°F. Lightly grease 8 cups of a standard muffin pan.
In a large bowl, combine the ground beef, egg, breadcrumbs, onion, milk, garlic powder, salt, and black pepper. Mix gently until just combined.
Divide the beef mixture among the 8 prepared muffin cups. Press it in lightly, leaving the tops slightly rounded.
In a small bowl, stir together the ketchup, balsamic vinegar, and brown sugar. Spoon about half of the glaze over the meatloaf muffins, reserving the rest.
Toss the carrots and zucchini with the olive oil. Spread them in a single layer on a rimmed baking sheet.
Put the muffin pan and baking sheet in the oven. Roast for 20 minutes, then brush the muffins with the reserved glaze. Continue baking until the beef is cooked through and the vegetables are tender, about 5 to 10 minutes more. The centers of the muffins should reach 160°F.
Let the muffins rest in the pan for 5 minutes. Serve with the roasted vegetables.