Heat 1 tablespoon of the olive oil in a large skillet over medium high heat.
Blot the surface of the pork chops dry and sprinkle with salt and pepper. In two batches, brown the chops about 5 minutes per side. Add the remaining oil for the second batch. Transfer to a platter and cover to keep warm.
Drain off any excess oil from the skillet and return it to the heat. Add the vinegar and chicken broth, stirring to loosen any brown bits from the bottom of the pan. Bring to a boil and reduce the liquid by half, about 3 to 4 minutes. once the liquid is thick and syrupy whisk in the butter. stir in the chopped sage and pour over the pork chops. Garnish with sage leaves.