Greek Stuffed Onions (Salantourmasi with Beef and Rice)

Ingredients

• 7 large yellow or white onions, about 3 lb (1.4 kg)
• 1 tablespoon kosher salt, for the boiling water
• 3 tablespoons olive oil
• 1 small onion or reserved onion centers, finely chopped
• 5 garlic cloves, minced
• 1 1/2 lb (680 g) lean ground beef
• 1 cup (200 g) Arborio or medium-grain rice, rinsed
• 1 cup (240 ml) tomato puree
• 1 1/2 cups (360 ml) reserved onion broth
• 1/3 cup chopped fresh parsley
• 2 tablespoons chopped fresh mint or 1 teaspoon dried mint
• 1 teaspoon dried oregano
• 1/2 teaspoon dried dill
• 1 1/2 teaspoons kosher salt
• 1/2 teaspoon black pepper
• 2 cups (480 ml) tomato puree
• 2 cups (480 ml) reserved onion broth
• 3 tablespoons balsamic vinegar
• 1/2 teaspoon kosher salt
• 1/4 teaspoon black pepper
• Chopped fresh parsley, for serving