Soak the bread in the ouzo for at least 5 minutes. Heat 3 Tbsp. of the olive oil in a skillet over moderate heat, add the onions, and cook for 5 minutes, stirring frequently, until they are soft but not brown. Remove the onions with a slotted spoon, placing them in a large mixing bowl. Squeeze the bread dry (discard the ouzo) and add the bread to the onions. Also add the ground beef, egg, mint, garlic, oregano, salt, pepper, and knead vigorously with your hands, then beat with a wooden spoon until the mixture is smooth and fluffy. Shape the beef mixture into balls about the size of walnuts (you may find that wetting your hands with water helps prevent sticking) and then roll the meatballs in the flour to coat evenly. Place the meatballs on a cookie sheet and refrigerate for at least one hour.
Add the remaining 4 Tbsp. of olive oil to a large skillet and brown the meatballs, 7 or 8 at a time, over high heat, cooking 8 to 10 minutes and shaking the pan from time to time. As each batch is done, remove them with a slotted spoon and place on an ovenproof serving platter. Keep them warm in a 200° F. (100° C) oven while you finish cooking the rest.
Serves 4 to 6 as an appetizer or first course (about 30 meatballs).