Heat oil in a heavy pot or Dutch oven. Add the alligator (or chicken) and let it brown. Don’t rush this part—you want those browned bits in the pot for flavor. Remove the meat after cooked.

Add the onion, bell pepper, and celery and cook until they soften. Stir in the garlic last so it doesn’t burn.

Stir in the tomato paste and let it cook a minute. Add the diced tomatoes, broth, bay leaves, paprika, thyme, cayenne, salt, and pepper. Stir everything together.

Return the meat to the pot, lower the heat, cover, and let it cook slow for about an hour or a little more, stirring now and then until the meat is tender and the sauce thickens.

Right before serving, squeeze in the juice of half to one lemon. Taste the sauce—it should brighten up the whole pot. If you like, add a little lemon zest too.

Spoon that rich, spicy sauce over hot rice and sprinkle with green onions or parsley.