How to Make It
Preheat the oven to 400°. In a saucepan of boiling salted water, cook the carrots until tender, 7 minutes. Using a slotted spoon, transfer to a plate. Add the spinach to the boiling water and cook just until wilted; drain well and add to the carrots.
In a large bowl, combine the beef with the pork, 2 cups of the bread crumbs, the pecorino, eggs, 1 teaspoon of salt and 1/2 teaspoon of pepper; mix well with your hands.
Line a work surface with a 15-inch-long sheet of plastic wrap. In a bowl, mix the flour with the remaining 1/2 cup of bread crumbs. Sprinkle half of the crumb mixture all over the plastic wrap. Transfer half of the meat loaf mixture to the plastic and press it into a 12-by-10-inch rectangle, about 1/2 inch thick. Lay half of the spinach leaves over the meat, leaving a 1-inch border on the short sides. Arrange half of the carrots over the spinach, and top with half the prosciutto and sliced cheese. Starting from the long end of the plastic wrap closest to you, tightly roll up the meat loaf, tucking in the filling and using the plastic wrap to guide you; discard the plastic. Repeat with another 15-inch sheet of plastic and the remaining bread crumbs, meat mixture, spinach, carrots, prosciutto and cheese. Drizzle each meat loaf with 2 tablespoons of oil.
Put the rosemary sprigs in the bottom of a broiler pan and pour in the red wine. Cover with the broiler pan grate. Set the meat loaves about 2 inches apart on the grate. Bake in the center of the oven for 40 minutes. Turn the broiler pan around and pour the water through the grate. Continue baking for about 35 minutes longer, or until an instant-read thermometer inserted in the center of each meat loaf registers 165°.
Transfer the meat loaves to a carving board and cover loosely with foil. Discard any cheese from the bottom of the pan and strain the pan juices into a small saucepan. Boil the pan juices over high heat until reduced to 1 cup, about 5 minutes. Pour into a serving bowl and season with salt and pepper.
Using a serrated knife, slice the meat loaves 1 inch thick and serve, passing the pan juices at the table.