In a bowl, toss the chicken with 1 tablespoon of the Cajun seasoning and a good pinch of salt and pepper. Let stand for 10 minutes while you slice the peppers and onion and mince the garlic.
Heat 1 tablespoon olive oil in a large Dutch oven over medium-high heat. Add half the chicken in a single layer and sear until lightly browned, about 2 minutes per side. Transfer to a plate and repeat with the remaining chicken, adding a drizzle more oil only if needed.
Reduce heat to medium and add the remaining 1/2 tablespoon olive oil. Add the peppers and onion with a pinch of salt. Cook, stirring occasionally, until the edges soften and pick up a little color, 4 to 5 minutes. Stir in the garlic, remaining 1 tablespoon Cajun seasoning, and smoked paprika; cook 30 seconds until fragrant.
Pour in the fire-roasted tomatoes and chicken broth, scraping the bottom of the pot to release any browned bits. Bring to a brisk simmer. Add the penne and stir well, pressing the pasta under the liquid. Cover and cook for 8 minutes, stirring once halfway through to prevent sticking.
Uncover, stir in the heavy cream, and cook at a lively simmer, stirring often, until the pasta is just al dente and the sauce is brothy-creamy, 4 to 6 minutes more.
Whisk the cornstarch with 2 tablespoons water. Return the chicken and any juices to the pot, then stream in the slurry while stirring. Simmer 2 minutes, until the sauce noticeably clings to the pasta.
Remove from heat and fold in the Parmesan, parsley, and lemon juice. Taste and season with additional salt and pepper as needed. Let the pot rest 2 to 3 minutes before serving so the sauce can thicken slightly.