Mix meat, egg, masa harina, salt, pepper, and vinegar in a bowl. Knead the ingredients and then make meatballs, about the size of a ping pong balls. Set aside.
In a large wide pot or Dutch oven, melt lard and add the flour and brown lightly to make a roux. Then add the chicken stock, green onions, chile, chopped tomatoes, tomato sauce, and garlic. Bring to a boil, then simmer for 15 minutes.
While the broth is simmering, drop each meatball into the broth and cook 30 minutes.