Combine milk and panko in a small bowl. Let sit 5 minutes.
In a large bowl, combine beef, mayo, soaked panko, grated onion, grated carrot, garlic, thyme, Dijon, tomato paste, Worcestershire, salt, and pepper.
Mix gently until just combined.
Transfer to a parchment-lined sheet pan. Shape into a 9x5-inch loaf.
Whisk together tomato paste, balsamic, maple syrup, Dijon, tamari, smoked paprika, garlic powder, onion powder, pepper, and water for glaze.
Preheat oven to 375°F.
Bake for 30 minutes.
Brush with half the glaze. Continue baking until internal temperature reaches 160°F — about 20–25 minutes more. Remove from oven. Brush with the remaining glaze.
Let rest 20 minutes before slicing.