1To make the filling: place the ham, carrot, roasted paprika, onions and garlic in a food processor. Transfer to a bowl, add the egg and bread crumbs.
2Place the pig, grease side down, on the work surface with 1 short end toward you. Using a sharp knife and starting 1/2 inch above the bottom of the roast, cut 1/2 inch along the right side. Continue cutting 1/2 inch on the underside, unrolling the pork.
3Preheat the oven to 400 degrees F. Place an oven rack in the center of the oven.
4Once the pork is in a flat piece, use a meat mallet to beat the pork so that most of the meat is in a uniform layer. Put the stuffing on the pork.
5Roll the pig, place the seam side down on the work surface. Tie the pork with cooking pita. Transfer the pork to a cauldron or a broiler pan.
6Rub the pork with the olive oil and then season with salt and pepper.
7Roast the pork at 400 degrees F until an instant reading thermometer inserted in the center of the loin 140-160 for about 1 hour and 30 minutes. Let the pork stand for at least 25 minutes before cutting.