In a large cast iron skillet, cook bacon until crispy.
Remove bacon from the skillet and place on a paper towel lined plate.
Keep bacon grease in skillet and add olive oil, if needed, to cook the chicken.
Carefully cut a pocket in each chicken breast and stuff it with the cheddar cheese. I used a block of cheddar cheese and cut the cheese into slices that fit into the chicken pockets. You can use a toothpick to keep it closed.
Heat the grease/oil over medium-high heat and add chicken breasts.
Cook chicken for 3-5 minutes on each side, until golden brown. They do not need to be cooked through.
Transfer browned chicken breasts to a plate.
With the remaining oil/grease, add the shallot and apple. Cook until apple is softened and shallots are translucent, about 5-7 minutes.
Add the garlic and cook one more minute.
Add the chicken broth and dijon, and whisk to combine. Season with salt and pepper.
Slowly add in the cream and thyme, stirring to combine. Add bacon back into the sauce, stirring to combine.
Return the chicken back to the skillet, tucking it into the sauce.
Bring the sauce to a simmer, then cover the skillet. Let cook over medium heat for another 8-10 minutes, until the chicken is cooked through. I always use a meat thermometer and cook my chicken until the middle reaches 165 degrees F. Cooking time will vary depending on the thickness of your chicken.
Serve chicken topped with sauce.