Pat chicken breasts dry and season generously with salt and black pepper. If any pieces are thick, butterfly or pound them to about 3/4 inch thickness for even cooking.

Heat olive oil and 1 tablespoon of butter in a skillet over medium-high heat. Sear the chicken for 4-5 minutes on each side until golden brown and cooked through. Remove the chicken and cover with foil to keep warm.

Reduce the heat to medium and add the remaining tablespoon of butter. Sauté the minced shallot for 2-3 minutes until softened, then add in the minced garlic and optional red pepper flakes, cooking for an additional minute.

Pour in the chicken broth, using a spatula to scrape any browned bits from the bottom of the skillet. Let it simmer for 1-2 minutes until slightly reduced.

Stir in the heavy cream, sun-dried tomatoes, and Italian seasoning. Allow the sauce to simmer, then reduce the heat and cook for 3-5 minutes to thicken.

Remove the skillet from heat and stir in the grated Parmesan cheese until melted and creamy. Taste and adjust seasonings as needed.

Slice the chicken against the grain or leave it whole, then return it to the skillet. Spoon the rich sauce over the chicken, garnishing with fresh basil or parsley and extra Parmesan if desired.