Pat pork chops with a paper towel to absorb any moisture. Season them with salt, pepper and brush or drizzle olive oil on each side.
Heat 1 tablespoon of butter in the skillet on medium high heat. When pan is hot and butter is sizzling place the chops in the pan, turn heat down to medium and leave them for 5 minutes. Turn them over and fry for another 4 minutes.
Remove chops from the pan and set aside.
Turn heat down to low and add the remaining tablespoon of butter and the diced shallots to the pan. Sauté for 5 minutes.
Add Dijon mustard and turn heat back up to medium. Pour broth, Rosemary and compote into skillet stirring well.
Add the pork chops back into the pan along with any juices that they may have released. Continue to cook pork chops for 5-8 more minutes or until done. If you feel like the sauce is evaporating too much, simply add more broth.
Serve with simple mashed or roasted potatoes.