Melt butter and olive oil in large pan over medium heat.
Add the peppers, and onion to same pan, until crisp-tender, about 4 minutes.
Add garlic and crushed red pepper to pan and sauté 3 minutes.
Add cream and chicken stock and mix in the Cajun spice blend.
Simmer until sauce thickens slightly, about 5 minutes.
Add basil and Parmesan cheese to sauce, stirring to incorporate.
Season sauce to taste with salt and pepper. Reduce heat to low, and simmer till the sauce thickens.