Place half of 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 for about 10 minutes until onions absorb all liquid.
Meanwhile, season the pork chops with salt, pepper and optional herbs de Provence.
Remove onions from skillet and add remaining oil and butter.
Cook pork chops for 4 minutes per side, until well browned. Add the onions back to the pan.
Stir the cornstarch into remaining broth and add to 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.)