Preheat your oven to 375°F (190°C).
Cook the penne pasta according to package instructions, draining when al dente.
In a large skillet, heat olive oil over medium heat and sauté the chicken until cooked through.
Add diced bell peppers and Cajun seasoning to the skillet, cooking for an additional 3-4 minutes.
Stir in the heavy cream and chicken broth, bringing the mixture to a simmer.
Combine the cooked penne pasta with the creamy Cajun mixture, stirring until well coated.
Transfer the mixture to a greased baking dish and top with shredded cheddar cheese.
Bake in the preheated oven for 25-30 minutes, or until golden and bubbly.
Remove from the oven and let it cool slightly before garnishing with chopped green onions.
Serve hot and enjoy your creamy Cajun chicken pasta bake!