Preheat the oven to 400 degrees F. Line a muffin tin with paper liners or lightly grease it. Line a separate baking sheet with parchment paper.
In a large bowl, combine the ground beef, breadcrumbs, egg, 1/4 cup ketchup, onion, garlic, Worcestershire sauce, salt, and pepper. Mix gently with your hands until just combined.
Divide the mixture evenly among 8 muffin cups, pressing it down lightly. Spread the remaining 2 tablespoons of ketchup over the tops of the muffins.
On the prepared baking sheet, toss the green beans and carrots with the olive oil, thyme, and a pinch of salt and pepper. Spread the vegetables into a single layer.
Place both the muffin tin and the baking sheet in the oven. Bake for 20 to 25 minutes, until the meatloaf muffins reach an internal temperature of 160 degrees F and the vegetables are tender with lightly browned edges.
Remove both pans from the oven. Let the muffins rest for 5 minutes before serving with the roasted vegetables.