Bring a large pot of salted water to a boil. Add 8 ounces of fettuccine pasta and cook according to package instructions until al dente. Drain and set aside, reserving about ½ cup of pasta water for the sauce.
In a large skillet, heat 2 tablespoons of olive oil over medium-high heat. Toss the chicken strips with 1 teaspoon of Cajun seasoning, salt, and pepper. Add the chicken to the hot pan in a single layer and cook until golden and cooked through, about 5-6 minutes. Remove the chicken from the skillet and set aside.
In the same skillet, add the diced onion and bell peppers. Sauté for 3-4 minutes until softened. Add the minced garlic and cook for another 30 seconds until fragrant.
Pour in 1 cup of chicken broth to deglaze the pan, scraping up any browned bits. Stir in 1 cup of heavy cream and bring to a gentle simmer. Let it cook for 3-5 minutes until slightly thickened.
Reduce the heat to low and stir in 1 cup of grated Parmesan cheese until melted and smooth. Taste and adjust seasoning with salt, pepper, and more Cajun seasoning if desired.
Return the cooked chicken to the skillet and toss to coat in the sauce. Add the drained fettuccine and gently toss everything together. If the sauce is too thick, add a splash of reserved pasta water to loosen it.
Sprinkle freshly chopped parsley on top for a burst of color and freshness. Serve immediately with extra Parmesan on the side.