Heat the olive oil in a large deep skillet or Dutch oven over medium-high heat. Add the turkey pepperoni and cook, stirring, until the edges crisp and curl, about 3–4 minutes. Remove with a slotted spoon and set aside — leave the rendered fat in the pot.

Season the chicken pieces with 1/4 teaspoon salt and the black pepper. Add to the pot in a single layer and sear until lightly golden on one side, about 4–5 minutes. It doesn't need to cook through here — it finishes in the sauce.

Stir in the onion, bell pepper, and mushrooms; cook until softened and the mushrooms release their liquid, about 4–5 minutes. Add the garlic, Italian seasoning, and red pepper flakes; cook 1 minute more, until fragrant. Season with the remaining 1/4 teaspoon salt.

Pour in the marinara and chicken broth, scraping up any browned bits. Stir in the uncooked penne. Bring to a lively simmer — the pasta cooks directly in the sauce, which is the one-pot enabler that keeps this at 30 minutes and means no draining.

Reduce the heat to medium-low, cover, and cook until the penne is just al dente and the sauce has thickened, about 11 minutes. Stir twice to keep the pasta from sticking. Return the chicken to the pot (it should already be cooked through — see doneness cues below).

Uncover, stir in 1 cup of the mozzarella and the Parmesan until melted. Sprinkle the remaining 1 cup mozzarella and the crisped pepperoni over the top, cover, and cook 2–3 minutes, until the cheese melts and bubbles. Shower with torn basil and serve.