Pat the chicken breasts dry and season both sides with salt, black pepper, and garlic powder.
Heat the sun-dried tomato oil in a large skillet over medium-high heat. Add the chicken breasts and sear for about 5 minutes per side, until golden. Transfer the chicken to a plate and set aside.
Reduce the heat to medium. Add the butter and chopped onion to the same skillet and cook for about 5 minutes, until softened and lightly golden.
Pour in the white wine and let it simmer for about 3 minutes, scraping up any browned bits from the bottom of the skillet.
Add the garlic and yellow mustard. Stir and cook for about 30 seconds, just until fragrant.
Reduce the heat to low. Stir in the chicken broth, heavy cream, thyme, oregano, red pepper flakes, and sun-dried tomatoes. Let the sauce simmer gently for a few minutes, until slightly thickened.
Stir in the grated Parmesan and fresh basil. Return the chicken breasts to the skillet and spoon the sauce over the top. Simmer gently for a few more minutes, until the chicken is cooked through and the sauce is creamy and smooth.