Place half of coconut oil and butter in a large skillet over medium heat. Add onions and saute for 3-4 minutes until translucent, then add 1/2 cup broth and the vinegar. Continue cooking until the onions absorb the liquid. Remove onions from skillet
Meanwhile, season the pork chops with salt, pepper, and herbs de Provence.
Add remaining oil and butter to the skillet. Cook pork chops for about 4 minutes per side, until well browned.
Add the onions back to the pan.
Stir arrowroot powder into the remaining broth and add to the pan. Continue cooking until the liquid is reduced by half and turns into a thick gravy.
Add one slice of mozzarella cheese (or 1/4 cup shredded) to each pork chop. If it doesn't melt easily, place a lid on the skillet to assist.
Notes
Cornstarch can be used in place of arrowroot powder, if desired.