Preheat the oven to 375°F and position a rack in the center.

Bring a large pot of salted water to a boil. Trim the root and stem ends off the onions, remove the skins, and cut a slit down one side of each so the layers can open flat. Boil until the onions are softened, 10 to 15 minutes, reserving the broth. When cool enough to handle, separate the large outer leaves, about 3 to 4 per onion, and save the inner centers for the sauce.

Heat the olive oil in a wide skillet over medium heat. Add the chopped onion and cook, stirring often, until translucent, about 5 minutes. Add the garlic and cook until fragrant, 1 to 2 minutes.

Increase the heat to medium-high and add the ground chuck. Cook, breaking it up with a spoon, until browned. Season with salt and pepper. Stir in the crushed tomatoes and bring to a simmer; cook until the sauce thickens slightly. Add the arborio rice and stir well to coat the grains.

Remove the skillet from the heat. Fold in the oregano, parsley, mint, and feta. Taste and adjust the salt and pepper.

Place 1 to 2 tablespoons of filling in the center of an onion leaf and roll it up like a shell, tucking the ends if possible. Arrange the rolls seam side down in a 9x13-inch baking dish, packed close together so they stay closed. You may need a second dish to fit them all.

In a large bowl or measuring cup, combine the tomato paste, 3 cups of reserved onion broth, and the reserved onion centers. Puree with an immersion blender until smooth. Season with salt and pepper. Pour the sauce over the onions, adding extra hot broth if it does not mostly cover them. Cover the dish tightly with foil.

Bake covered for 1 hour. Remove the foil and continue baking for 30 minutes, until the sauce has thickened and the onions are caramelized. Broil for a minute or two at the end, watching closely, if you want more color.

Serve warm with pita and additional feta on the side.