Boil the halved onions in water with 3 tablespoons of the vinegar until soft but not falling apart, about 15 minutes.
Put the chopped onions, carrots and celery in a food processor and blend until finely chopped. Combine the vegetable mixture, ground beef, oats, rice, tomato sauce, cold water, paprika, vegetable herb seasoning, chicken base, garlic and pepper in a bowl and mix well with your hands.
Remove the halved onions from the water and separate into cups. Fill each cup with meat mixture and place meat-side up in a single layer in a 12- by 15-inch baking pan. Mix the remaining 2 tablespoons vinegar with enough hot water to pour into the pan to cover halfway up the sides. Cover and bake for 2 hours.
To serve, transfer the stuffed onions to plates and cover with sauce. Serve with a cold sour cream and cucumber salad.