Cut chicken breast into bite-sized pieces and toss with 2 tablespoons cajun seasoning until evenly coated. Heat olive oil in a large skillet over medium-high heat. Add seasoned chicken in a single layer without crowding. Cook 5-6 minutes, flipping once, until golden brown and cooked through. Remove chicken to a plate and set aside.

In the same skillet, add butter over medium heat. Add sliced bell peppers and diced onion. Cook 4-5 minutes, stirring occasionally, until vegetables soften and get some color. Add minced garlic and remaining 1 tablespoon cajun seasoning. Cook 30 seconds until fragrant, stirring constantly so garlic doesn't burn.

Pour chicken broth into the skillet and scrape up any browned bits from the bottom with a wooden spoon. Let simmer 2 minutes to reduce slightly. Lower heat to medium-low and pour in heavy cream. Stir in tomato paste until fully combined. Add grated parmesan cheese gradually while stirring constantly until melted and smooth. Season with salt and black pepper to taste. Let sauce simmer gently 3-4 minutes until thickened enough to coat a spoon. Don't let it boil or the cream will break.

While sauce simmers, cook pasta in salted boiling water according to package directions until al dente. Drain pasta, reserving 1 cup pasta water. Add cooked pasta to the creamy cajun sauce in the skillet. Toss until every piece is coated. Add cooked chicken back to the pan with any accumulated juices. If sauce is too thick, add pasta water a splash at a time until desired consistency. Toss everything together over low heat for 1-2 minutes. Taste and adjust seasoning with more cajun spice, salt, or pepper if needed. Garnish with fresh chopped parsley and extra parmesan before serving.