Consider sound when cooking this dish. The andouille sizzles loudly at first, then quiets as it renders fat, indicating that it's nearly done. The vegetables cook softly as they release liquid. But the noise increases as they start to caramelize. Don't worry if the bottom of the pan becomes dark brown or even black in parts before you add the broth; it deepens the flavor of the dish.
6 servings (serving size: 1 1/3 cups)
Heat oil in a large Dutch oven over medium-high heat. Add sausage; cook until sizzling quiets (about 8 minutes), stirring occasionally.
Add bell pepper, onion, celery, and bay leaves; cook until vegetables are golden brown, sizzle loudly, and begin to squeak (about 14 minutes), stirring occasionally. Add chicken and next 8 ingredients (through garlic); cook 4 minutes, stirring occasionally.
Add tomato puree; cook 2 minutes, stirring occasionally. Add broth, and bring to a boil. Stir in rice. Cover, reduce heat, and simmer 20 minutes. Discard bay leaves. Stir in green onions.