Heat the oven to 375 degrees and line a large baking sheet with parchment paper.
In a mixing bowl, combine the ground beef, breadcrumbs, egg, milk, onion, garlic, 2 tablespoons ketchup, Worcestershire sauce, salt, and pepper. Mix until just combined, then shape into a loaf and place it in the center of the baking sheet.
Spread the remaining tablespoon of ketchup over the top of the meatloaf.
In the same bowl, toss the halved potatoes and green beans with olive oil, thyme, and paprika until evenly coated.
Arrange the vegetables around the meatloaf on the baking sheet in a single layer.
Bake for 45 to 50 minutes until the meatloaf reaches 160 degrees inside and the potatoes are golden at the edges.
Remove from the oven and let the meatloaf rest for 5 minutes before slicing.