Brown the sausage. Heat 1 tablespoon of the olive oil a large Dutch oven or soup pot over medium heat. Add the sausages and brown on all sides. Remove from pot and set aside to cool slightly.

Saute vegetables. Add remaining oil, onions, celery, and garlic to the pot and season with salt and pepper. Cook, stirring occasionally, until tender and starting to brown. Add green tomatoes, bay leaf, oregano, allspice, and chicken stock.

Simmer. Slice the cooled sausages in half lengthwise, then in 1/2-inch thick half-moon slices. Add to the pot and bring the soup to a boil. Reduce the heat to low and simmer for about 45 minutes. Taste and add more salt and pepper as needed.

Serve. To serve, divide cooked rice between the bowls and ladle the hot soup on top.