1 To make the sauce: Heat the oil in a medium saucepan over medium heat. Add the red onion and garlic and cook, stirring occasionally, until the onion is translucent, about 4 minutes. Add the wine and bring to a boil. Stir in the pureed tomatoes, 1 cup water, and mint and bring to a boil. Reduce the heat to low and simmer, stirring occasionally, to blend the flavors, about 20 minutes. The sauce should remain somewhat liquid as it will reduce more when cooked with the meatballs and the additional sauce will distribute the heat and encourage even cooking. Season to taste with the salt and pepper. Remove from the heat.
2 Meanwhile, make the meatballs: Using clean hands, mix the ground beef, lamb, bread crumbs, yellow onion, garlic, parsley, mint, Pecorino, yolks, salt, and pepper in a large bowl. Using about a tablespoon for each, roll the mixture into 36 meatballs and transfer the balls to a baking sheet.
3 Heat the oil in a very large skillet over medium-high heat. In batches without crowding, add the meatballs and cook, turning occasionally, until browned all over, about 6 minutes, adding oil as needed. Using a slotted spoon, transfer the meatballs to a platter. Pour out the fat in the pan.
4 Add the sauce to the skillet and bring to a simmer, scraping up the browned bits with a wooden spoon. Return the meatballs to the sauce and reduce the heat to low. Partially cover the skillet and cook, occasionally stirring the sauce, until the meatballs are tender, about 30 minutes. If the sauce is reduced too much, stir in enough water to loosen it. Transfer the meatballs and the sauce to a deep platter. Serve hot, with the Pecorino on the side.