In a large skillet, melt 2 ounces of butter and 1/2 cup of olive oil over medium-high heat. Sauté the onions, bell peppers and mushrooms for 4–5 minutes. Add white wine and reduce the heat by half. Add minced garlic, thyme, basil, 1 teaspoon of black pepper and cayenne pepper. Let this mixture cook for 1–2 minutes, then whisk in the flour, stirring constantly until white roux is achieved. The flour will absorb all of the liquid in the skillet. Slowly add heavy whipping cream, stirring constantly until desired thickness. Fold in artichoke hearts and let it simmer for 2–3 minutes.
In a separate skillet, add the remaining 2 ounces of butter and 1/2 cup of olive oil. Sauté the shrimp for 2 minutes or until pink and curled. Add lemon juice, salt and pepper to taste and parsley. Cook for 4–5 minutes.
Add the sautéed shrimp with juice to cream sauce, stirring to incorporate. Once everything is thoroughly mixed, serve your dish over rice or pasta.