Preheat the oven to 350°F.
In a large bowl, beat the eggs. Add the milk and torn bread pieces. Let it sit for a few minutes until the bread absorbs all the liquid.
Add the chopped onion, grated carrot, shredded cheddar cheese, chopped parsley, salt, thyme, and black pepper to the bowl. Mix until well combined.
Add the lean ground beef and ground pork to the bowl and mix until fully incorporated.
Line a loaf pan with plastic wrap and transfer the meatloaf mixture into the pan. Press down to shape the meatloaf into the loaf pan.
Invert the loaf pan onto a foil-lined baking sheet, then carefully remove the plastic wrap.
Bake the meatloaf in the preheated oven for 45 minutes.
Meanwhile, prepare the topping by combining the tomato sauce, brown sugar, and yellow mustard in a small bowl.
After 45 minutes of baking, spoon the topping over the meatloaf. Return it to the oven and bake for an additional 30 minutes, or until no longer pink in the center. Baste the meatloaf with the topping halfway through the baking time.
Remove the meatloaf from the oven and let it stand for 10 minutes before serving.