Soak the bread in water for 5 minutes, remove from the water and press out the liquid by hand. Place the soaked bread in a large bowl, add the beef and the sausage and mix by hand to combine. Add the garlic, basil, eggs and pecorino and mix well to combine. Make golf ball-sized balls out of the meat mixture and set aside.

In a large, heavy-bottomed skillet, heat 1 cup oil until smoking. Cook the meatballs in the oil until golden brown and cooked through, working in batches if necessary to avoid overcrowding the pan. Remove the meatballs to a plate lined with paper towels and keep warm.

In the work bowl of a food processor, puree the remaining 1/2 cup oil, anchovies, capers, parsley, mint and white vinegar. Pour half of the sauce over the warm meatballs, and serve the other half on the side.