Pat chicken dry, season with salt, pepper, and Italian seasoning.
Sear chicken in sun-dried tomato oil until golden on both sides, then transfer to the crockpot.
Deglaze the skillet with a splash of broth and pour into the crockpot.
Add remaining broth, sun-dried tomatoes, garlic, and red pepper flakes around the chicken.
Cover and cook on LOW for 4 to 5 hours or HIGH for 2 to 3 hours, until chicken is fork-tender.
Stir in heavy cream and Parmesan, then let sit on warm for 15 minutes, stirring occasionally.
Top with fresh basil and serve immediately.