Step 1

In a medium bowl, combine the beef, 2 tablespoons oil, ¼ cup of the grated onion, half of the garlic, 1½ teaspoons of the allspice, the red pepper flakes, 1 teaspoon salt and ½ teaspoon black pepper. Mix with your hands until well combined; set aside.

Step 2

In a large pot, combine the remaining 2 tablespoons oil, the remaining onion, the remaining garlic, the remaining ½ teaspoon allspice and ½ teaspoon salt. Cook over medium-high, stirring occasionally, until the mixture is browned and sticks to the pot, about 5 minutes.

Step 3

Add the tomatoes with juices, the broth and 2 cups water. Bring to a simmer, scraping up any browned bits, then stir in the rice. Reduce to medium and cook, uncovered and stirring occasionally, for 8 minutes; the rice will not be fully cooked.

Step 4

Using dampened hands, pinch off a 1-tablespoon portion of the meat mixture, form it into a ball and drop it into the broth. Shape the remaining meat mixture and add to the pot in the same way; it’s fine if the meatballs are not completely uniform. Simmer, uncovered and stirring occasionally, until the soup is slightly thickened and the center of the meatballs reach 160°F, 10 to 15 minutes. Off heat, taste and season with salt and black pepper.