Season the chicken with 2 tsp of Cajun seasoning, ½ tsp salt, and pepper
Cook the pasta in a large pot of salted boiling water until al dente, according to package instructions. Reserve ½ cup of cooking water, drain, and set aside.
Heat a large skillet over medium-high heat and melt the butter with ½ tbsp olive oil. Brown the chicken breasts for 3-4 minutes on each side until cooked through. Transfer to a plate. Let stand for a couple of minutes and cut into slices.
Heat the remaining ½ tbsp of oil in the same skillet over medium-high heat and saute the onion and garlic until fragrant, about 2 minutes, scraping all the bits and pieces stuck to the bottom.
Mix in the heavy cream, sun-dried tomatoes, green onions, basil, parsley, ½ tsp salt, and pepper to taste. Simmer until slightly thick, about 2 minutes. If the sauce is too thick, add a splash of the reserved pasta cooking water.
Add the sliced chicken and drained pasta into the skillet and toss to coat everything in the sauce. Serve with grated Parmesan cheese and extra sliced green onions on top.