Pat the chicken breasts dry with paper towels and season generously on both sides with salt and pepper. Heat the olive oil in a large skillet over medium-high heat. Sear the chicken breasts for about 5-7 minutes per side, until golden brown and cooked through. Remove the chicken from the skillet and set aside on a plate. Tent loosely with foil to keep warm.

Reduce the heat to medium. Add the butter to the same skillet. Once melted, add the chopped onion and sauté until softened and translucent, about 5 minutes. Add the minced garlic and cook for another minute until fragrant, being careful not to burn it.

Stir in the chopped artichoke hearts and sun-dried tomatoes. Cook for 2-3 minutes, allowing them to heat through and meld with the onion and garlic.

Pour in the heavy cream and chicken broth. Bring the mixture to a simmer, scraping up any browned bits from the bottom of the skillet. Let it simmer gently for about 5-7 minutes, or until the sauce has thickened slightly.

Stir in the grated Parmesan cheese, chopped basil, and chopped parsley. Season the sauce with salt, pepper, and red pepper flakes (if using) to your taste. Continue to simmer for another 1-2 minutes until the cheese is melted and the sauce is smooth.

Return the seared chicken breasts to the skillet, nestling them into the sauce. Spoon some of the sauce over the chicken. Let it simmer for 2-3 minutes to allow the chicken to heat through and absorb the flavors.

Serve immediately, spooning extra sauce over the chicken.