Preheat oven to 350°F. Grease or line a 9x5-inch loaf pan for easy cleanup.
Combine wet ingredients. In a large bowl, whisk together eggs, milk, salt, and pepper until well mixed.
Add the binder. Stir in the crumbled bread and let it soak for a minute to absorb the liquid. This keeps the loaf tender.
Mix in the good stuff. Add the ground beef, onion, carrot, and Cheddar. Mix gently with a fork or clean hands until just combined. Don’t overwork it or the loaf can become dense.
Shape and pan. Press the mixture evenly into the prepared loaf pan. For crispier edges, form it into a loaf on a parchment-lined baking sheet instead.
Make the glaze. In a small bowl, mix the brown sugar, ketchup, and mustard until smooth. Spread evenly over the top of the meatloaf.
Bake for about 60 minutes, or until the center reaches 160°F.
Rest before slicing. Let it stand 5–10 minutes so the juices redistribute. This keeps your slices moist and tidy.