Combine the bread and buttermilk in a small bowl. Let sit for 10 minutes, mashing occasionally with a fork, until a smooth paste forms.
Place the ground meat, cheese, parsley, egg yolk, garlic, salt, and pepper to taste in a medium bowl. Add the bread-milk mixture and combine until evenly mixed.
Shape 3 tablespoons of the mixture into a 1 ½-inch round meatball, or use the ice cream scoop to form the balls. (When forming meatballs, use a light touch. if you compact the meatballs too much, they can become dense and hard.). This should get you about 14 meatballs.
Pour the vegetable oil into a 10 or 11 inch sate pan to a depth of ¼ inch. Turn the heat to medium-high. After several minutes, test the oil with the edge of a meatball. When the oil sizzles, add the meatballs in a single layer.
Fry, turning several times, until nicely browned on all sides, about 10 minutes. Regulate the heat as needed to keep the oil sizzling but not smoking. Transfer the browned meatballs to a plate lined with paper towels and set aside.
Meanwhile, bring 4 quarts water to a rolling boil in a large pot.