In a large bowl, whisk together the milk and bread crumbs. Stir in the eggs, cheese, basil, salt, and pepper. Add the ground beef and mix until incorporated (don’t overmix). Using an ice-cream scoop, scoop a mound of meat mixture into the palm of your hand and roll it into a ball about the size of a golf ball; if they’re larger they won’t cook through. Repeat until all the meat mixture is used.
In a large cast-iron skillet, add enough oil to come about 1 inch up the sides of the pan. Heat over medium-high heat until hot. To test if the oil is ready, stick a wooden spoon into the oil; it’s hot enough when tiny bubbles form around the edge of the spoon. Working in batches, carefully add meatballs to the skillet, leaving room to flip them. Fry for 2 minutes on all sides, turning them until the outside of the balls are golden brown. Repeat until all the meatballs are cooked. Transfer to a platter to serve.