Bring a large pot of salted water to a boil. Cook the rigatoni until just al dente according to the package directions. Reserve about ½ cup of pasta water, then drain the pasta and set aside.
Season the chicken pieces with salt, pepper, and smoked paprika. In a large, deep skillet or Dutch oven, heat 1 tablespoon of olive oil over medium-high heat. Add the chicken in a single layer (work in batches if necessary) and cook until the chicken is nicely browned on all sides—about 4–5 minutes per batch. Transfer the chicken to a plate and set aside.
In the same skillet, lower the heat to medium and add the remaining 1 tablespoon of olive oil. Toss in the sliced onion and both bell peppers. Sauté for about 5 minutes until they begin to soften. Then add the minced garlic and red pepper flakes, cooking for another 30 seconds until fragrant.
If using, pour in the white wine to deglaze the pan, scraping up any browned bits from the bottom. Let the wine reduce slightly (about 1 minute). Stir in the diced tomatoes and chicken broth, and bring the mixture to a simmer.
Return the browned chicken (with any juices on the plate) to the skillet. Let everything simmer together for about 5–7 minutes, allowing the chicken to finish cooking and the flavors to meld.
Reduce the heat to low, then stir in the heavy cream and grated Parmesan cheese. Allow the sauce to heat through and thicken slightly—this should take about 3–4 minutes. If the sauce seems a bit thick, add a splash of the reserved pasta water to loosen it up. Taste and adjust the seasoning with more salt and pepper if needed.
Add the drained rigatoni to the sauce, gently tossing to coat every piece of pasta with that luscious, spicy cream sauce. Sprinkle freshly chopped basil or parsley over the top for a burst of color and freshness.