Dice one of the onions and shred carrot. Sauté the veggies until softened and blend them until smooth. In a large mixing bowl, combine the blended veggies with the ground meat.
Using a food processor or blender, blend the other onion and add it to the meat mixture.
In a separate dish, soak the bread slices in milk for about 10 minutes. Using your hand, squeeze out as much milk as you can from the bread and crumble it into the meat mixture. Add cheese to the meat mixture and season it with salt and pepper.
Using your hands, mix the ingredients together until well-combined.
Form meat patties into oval-shapes about the size of your hand. Over high-heat, fry each side just until they are browned (about 1 minute per side).
Transfer the meat patties to a shallow baking dish and cover them loosely with foil. Bake at 300°F for 30 minutes.