Cut off the ends of onions and peel off the papery layers. Place the onions into a Dutch oven or a large pot, cover with water, and add 1/4 cup vinegar. Bring to a boil and cook until soft but not falling apart, about 15 minutes. Remove the onions from the water and let them cool enough for handling.
Separate onion layers without tearing by gently squeezing out ring after ring (see recipe notes for tips). Set aside the larger rings and chop the smaller, inside rings.
In a medium bowl, combine 1 pound ground beef, 1/3 cup rice, one egg, 2 minced garlic cloves, 1 tablespoon tomato paste, 1 teaspoon sweet paprika, 1 tablespoon chopped fresh parsley, 1 tablespoon salt or Vegeta, and 1/2 tablespoon black pepper. Mix gently with clean hands until just incorporated.
Fill onion rings with meat mixture until all stuffing is used.
Preheat oven to 375 degrees Fahrenheit. Grease a casserole pan with two tablespoons of vegetable oil. Place some of the chopped onions on the bottom of the prepared pan and layer with stuffed onions.
Pour enough water to come up about an inch from the top, cover, and bake for about 40 minutes, turning the onions over once halfway through the baking.
Grease a large pot with oil and cover with some of the remaining chopped onions. Layer the stuffed onion rings into the pot by placing them tightly next to each other. Top with more chopped onions (you don't have to use them all) and add enough water to cover the onions.
Cover the pot with lid and cook for 30 minutes over medium-low heat until soft and rice is cooked.
To serve, transfer the stuffed onions onto plates and pour with sauce. Serve drizzled with lemon juice and a dollop of sour cream alongside crusty bread.
Onions of the same size and shape ensure even cooking time.
To pry out the onion rings, gently push the center in, and the outer layer will pop out. To help the process, loosen the thin skin between the layers with your finger (*or see the post for a different method). Once the rings are separated, peel off the inner skin (called epidermal cell wall). See the step-by-step photos in the post.
Instead of vegetable oil, use olive oil or oil of choice.
Cover the stuffed onions with beef stock instead of water. If using water, season it with salt, pepper, and paprika.
You can also add a light roux to the onions for the last 10 minutes of cooking if you prefer a thicker sauce.