Pat the pork chops dry with paper towels and season both sides with salt and pepper.
Place oil in a cast-iron skillet or other heavy bottomed pan over medium-high heat until it appears to be shimmering. Add seasoned pork chops to pan and cook until browned and cooked through, 5-6 minutes per side for medium. Transfer pork chops to a plate and cover with foil to keep warm.
Add the ham to the skillet. Cook, stirring frequently, until the ham is fragrant and any fat has rendered, about 5 minutes.
Add the coffee and bring to a boil. Continue to boil until the coffee has reduced by half.
Stir in the chicken broth and sugar, return to a simmer, and continue to cook for 5 minutes.
Remove from the heat and stir in the butter and parsley.
Spoon the gravy over the pork chops and serve immediately.
