Preheat oven to 350°F.
If using a loaf pan, spray it with nonstick cooking spray. If using a sheet pan, line it with foil.
Combine breadcrumbs and milk in a large bowl and set aside to soak.
Combine onions, carrots, and garlic in the bowl of a food processor and pulse until finely chopped (the largest pieces should be about the size of a pea). (Note: If you prefer, you can also finely chop these by hand.)
Melt butter in a large saute pan over medium heat.
Add onions, carrots, and garlic with a pinch of salt.
Saute until vegetables are soft, about 5 minutes.
Set aside to cool for 5 minutes.
To breadcrumbs and milk, add beef, egg, parsley, Worcestershire sauce, salt, and black pepper.
Top with cooked carrots and onions.
Using your hands, gently mix everything together until just combined. (Try not to over mix or this will make your meatloaf more tough.)
Gently shape the meat mixture into a loaf shape and transfer to loaf pan or sheet pan.
Transfer meatloaf to oven and bake for 55 to 60 minutes (use an instant read thermometer if you have it - the center will register 155°F when the meatloaf is done).
While meatloaf cooks, whisk together ketchup, brown sugar, and mustard.
Remove meatloaf when it has about 20 minutes left to cook and spread glaze over top.
Rest meatloaf for 10 minutes then slice and serve.