Preheat oven to 375°F and set the rack to the middle level. Bring a large pot of salted water to boil. Cut off the tops and bottoms of the onions and remove the skin. Make a slit down 1 side of each onion to prepare for stuffing. Boil the onions until soft (about 10-15 minutes) and save the onion broth.

Once the onions can be handled, separate the largest outer layers (approximately 3-4 per onion). Save the onion centers for the sauce.

Heat the olive oil in a large pan over medium heat. Add the diced onion and cook until soft, then add the garlic and cook for another 2 minutes.

Add the ground beef and mix to combine. Turn the heat to medium-high and cook the beef until it begins to brown. Season with salt and pepper. Add the tomatoes and simmer until the sauce thickens.

Once the sauce thickens, add the rice and mix well to combine. Remove the pan from the heat and mix in the oregano, parsley, mint, and feta cheese. Taste and season with more salt and pepper if needed.

Scoop about 1-2 tablespoons of the filling and place it in the center of an onion piece. Roll like a shell and place seam side down in a 9×13 baking dish. Repeat for the remaining pieces, arranging the stuffed onions close together to prevent opening.

In a large measuring cup or bowl, combine the tomato paste with 3 cups of onion broth and 1 cup of the chopped onion centers. Puree until smooth. Pour the sauce into the baking dish until it mostly covers the stuffed onions. If needed, add more hot onion broth. Cover the dish tightly with foil.

Bake for 1 hour covered, then remove the foil and bake for another 30 minutes or until the liquid has thickened and the onions have caramelized. Broil for a couple of minutes if needed but watch carefully.

Serve with pita and more feta on the side.