Preheat the oven to 350°F (180°C).
Heat olive oil in a sauté pan over medium heat. Add the diced carrot and onion with a small pinch of salt, and cook for 5 minutes until softened and starting to take on some color. Set aside to cool.
In a large bowl, mix together the ground beef, salt, black pepper, garlic powder, and thyme.
Sprinkle the breadcrumbs over the top, then add the parmesan, milk, egg, ketchup, and Worcestershire sauce.
Mix thoroughly until everything is fully combined and the texture is soft and even.
Once the veggies are cool enough to handle, add them to the meat mixture and mix again until well incorporated.
To make the glaze: In a separate bowl, whisk together the ketchup, brown sugar, balsamic vinegar, Worcestershire sauce, salt, garlic powder, and black pepper.
Divide the mixture into 6 equal portions. Shape each one into a tight, tall mini loaf and place on a foil-lined baking sheet.
Brush the glaze over the tops and sides of each loaf and bake for 20 minutes.
Remove from the oven, brush on a second layer of glaze, and return to the oven for another 25 minutes, or until the centers reach 160°F (71°C).
Allow to rest for 15 minutes before serving.