Slice chicken breast fillets horizontally. Season both sides of the chicken with salt, pepper, garlic, and herb seasoning, and set aside.
Preheat olive oil over medium-high heat in a shallow Dutch oven or deep-sided skillet. Once the oil is shimmering, add the chicken and sear until golden brown on both sides. Remove to a plate.
Add a drizzle of the sun-dried tomato oil along with the butter and garlic, saute for about 30 seconds, add the stock and cream, sprinkle a little garlic and herb and a few leaves of torn basil, and bring to a gentle boil, add the seared chicken back in (along with any juices collected in the plate), sun-dried tomatoes, partially cover, and cook about 10 minutes.
Adjust seasoning to taste, stir in the parm and serve the chicken on the bed of something cosy that absorbs all that delicious sauce.