Step 1Pat any moisture from the surface of the chops. Season with the salt and pepper.
Step 2Heat the oil and butter in a large, heavy skillet over medium high heat. Add the pork chops to the skillet and sear until both sides are nicely browned, about 3 to 4 minutes each side. Remove the chops from the skillet to a plate cover and keep warm.
Step 3Reduce the heat to low. Pour out all but 1 tablespoon of fat from the skillet. Add the shallots, carrots and celery and quickly saute for about 1 to 2 minutes. Add the white wine and stir to deglaze the pan, scraping up the brown bits from the bottom.
Step 4Stir in the chicken broth. Bring the sauce to a simmer; cook until reduced by half.
Step 5Add the pork chops back into the skillet along with any drippings and simmer, spooning the juices over the chops as they cook, 1 to 2 minutes or until the chops are firm and just pink in the center. Remove the chops from the skillet.
Step 6Add the butter, tilting the pan and swirling the butter until the sauce is slightly thickened. Serve each chop with a little sauce spooned over the top.