Some old‐fashioned jambalaya recipes start with a pound each of pork, ham, and sausage, and finish with shrimp. If you want to add good ham and sausage, do so at the beginning, along with the onions—I suggest a total of a pound or so.
Place the olive oil in a medium‐to‐large casserole and turn the heat to medium‐high. Add the onions and bell pepper, sprinkle with salt and pepper, and cook, stirring occasionally, until the onion softens and just begins to brown, about 10 minutes. Warm the stock in a small saucepan over medium heat.
Stir in the garlic, cayenne, and thyme, and stir for about 30 seconds. Add the tomatoes and turn the heat to medium‐high. Cook, stirring, for 5 minutes, or until the tomatoes begin to break up.
Stir in the rice, then the stock. Bring to a boil, turn the heat to medium, and cook, uncovered, stirring occasionally, until the rice is tender and the liquid just about absorbed, 20 to 30 minutes.
Add the shrimp and stir. Cook 2 or 3 minutes, then raise the heat if necessary to cook off the remaining liquid. Garnish and serve.