Bring a large pot of salted water to a boil. Add the 8 oz of bowtie pasta and cook according to the package instructions until al dente, usually about 10-12 minutes. Drain the pasta and set aside, reserving about 1/2 cup of pasta water for later.
While the pasta cooks, heat 1 tablespoon of olive oil in a large skillet over medium-high heat. Add the cubed chicken breasts and season with salt, pepper, and 1 tablespoon of Cajun seasoning. Cook the chicken until browned and cooked through, about 5-7 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add diced onion, garlic, red bell pepper, and green bell pepper. Sauté until the vegetables are tender and fragrant, about 4-5 minutes.
Pour in 1 cup of chicken broth and 1 cup of heavy cream into the skillet with the sautéed vegetables. Stir well and bring the mixture to a gentle simmer. Allow it to thicken slightly, about 3-4 minutes.
Return the cooked chicken to the skillet. Add the drained bowtie pasta and 1/2 cup grated Parmesan cheese. Toss everything together, adding a splash of reserved pasta water as needed to loosen the sauce and coat the pasta evenly.
Taste and adjust seasoning with salt, pepper, or additional Cajun seasoning if desired. Sprinkle freshly chopped parsley on top for a bright, fresh finish, and serve immediately.