Heat the olive oil in a large deep skillet over medium-high heat. Add the sliced andouille and cook, stirring occasionally, until browned at the edges and the fat renders, about 4 minutes. This browning step is the flavor enabler — those caramelized bits become the backbone of the whole dish. Transfer the sausage to a plate, leaving the rendered fat in the skillet.

Season the chicken pieces with 1/2 teaspoon salt and the black pepper. Add to the hot skillet and sear, stirring once, until golden on the outside but not yet cooked through, about 3 minutes. Transfer to the plate with the sausage.

Add the onion, bell peppers, and celery to the skillet. Cook, stirring, until softened, about 3 minutes. Stir in the garlic and Cajun seasoning; cook 1 minute more, until fragrant.

Pour in the diced tomatoes with their juices and the chicken broth, scraping up any browned bits. Stir in the uncooked penne. The penne cooks directly in the pot — that’s the one-pot enabler, and it means every piece of pasta absorbs Cajun-spiced tomato broth instead of plain water.

Bring to a lively simmer, then reduce the heat to medium-low, cover, and cook until the penne is just al dente, about 10 minutes. Stir once halfway through to keep the pasta from sticking. Uncover and stir the chicken and sausage back in; simmer 1–2 minutes more, until the chicken is cooked through and the sauce is thick but still saucy. Stir in the green onions and the remaining 1/2 teaspoon salt; taste and add hot sauce if you like it spicier.

Spoon into bowls and finish with more sliced green onions and a few dashes of hot sauce, if desired. Serve right away — the penne keeps absorbing sauce as it stands.