Preheat the oven to 425 degrees . Place the potatoes in a pot, cover with cold water and cover the pot with a lid. Bring to a boil, then salt the water and cook the potatoes until tender, 12 to 15 minutes. Drain the potatoes and add them back to the pot.
While the potatoes are working, in a large bowl, combine the ground meats with 1/2 cup cheese, 1/2 cup bread crumbs, a splash of cream, the egg, parsley, half of the chopped garlic, the Worcestershire sauce and allspice; season with salt and pepper. Drizzle 1 tablespoon EVOO onto a baking sheet, form the meat mixture into 4 loaves about 1 to 1 1/2 inches thick and place on the baking sheet. Drizzle with 1 tablespoon EVOO. Bake the loaves for 20 minutes.
While the meat loaves bake, in a large skillet, heat the remaining 2 tablespoons EVOO, 2 turns of the pan, over medium heat. Add the remaining garlic, the carrot, onion leaf and cook until tender, 7 to 8 minutes; season with salt and pepper and the rosemary. Stir in the tomato paste and cook for 1 minute. Whisk in the broth and simmer until thickened. Discard the bay leaf.
Add the remaining 1/3 cup cream and 1 cup cheese to the potatoes and season with 1 teaspoon salt; smash to desired consistency. Divide the potatoes among 4 plates and make a small well in the center. Remove the meat loaves from the oven, turn in their sauce and set alongside the potatoes. Spoon extra sauce into the wells and over the meat loaves.