Combine honey, dijon, 1/2 tsp salt and 1/4 tsp pepper in a large zipper bag. Place chicken in bag, seal and toss to coat chicken. Let marinade at least 15 minutes.
Melt butter in a skillet over medium heat. Add chicken and cook for 7-8 minutes on each side until nice and brown. Reserve marinade. Transfer chicken to a plate.
In a small bowl, dissolve the cornstarch in 3 Tbsp of chicken broth
To the pan, add in remaining chicken broth, thyme, sour cream, half and half, cornstarch mixture, remaining marinade** (see note below) and 1/4 tsp of salt. Stir well, scraping bottom to release the brown bits on the bottom of the pan.
Add chicken back to pan and cook until chicken has reached 165 degrees internal temperature and the sauce has thickened.
Sprinkle with parsley and serve.
Notes
NOTE: Cooking the marinade in the skillet will kill off any bacteria from the raw chicken.