Step 1In a medium bowl, combine the ground beef, egg, salt, pepper, ketchup, bread crumbs and water. Roll a heaping tablespoon into a 1-inch meatball, continuing until all of the mixture is used. You should have about 3 1/2 dozen meatballs.
Step 1In a large, heavy-bottom skillet, heat 1 tablespoon oil over medium-high heat. Fry half of the meatballs until golden brown on all sides. Strain the meatballs into a clean bowl, then wipe out the skillet with a paper towel and repeat with the remaining oil and meatballs. Strain the remaining meatballs into the bowl, this time leaving the fat in the pan.
Step 2Reduce the heat to medium, and stir the onions and garlic into the fat. Cook until the onions are soft but not browned, 3 to 5 minutes. Stir in the bitters, broth, mustard, flour, bourbon, vermouth and oregano and bring to a boil. Cook over high heat, stirring occasionally, until the sauce thickens and is reduced to 1 1/4 cups, about 5 minutes.
Step 3Return the meatballs to the pan and stir into the sauce. Simmer just until the meatballs are warmed through, about 5 minutes. Stir in the parsley and serve immediately, or refrigerate and reheat before serving.