Pat pork chops dry with paper towels, and season with salt and pepper.

Melt butter in a large, nonstick skillet over medium heat. Add olive oil and stir to combine.

When butter and oil shimmer, carefully add chops and cook over medium heat until browned on one side, 5 to 6 minutes. Turn and cook pork chops until no longer pink in the center and browned on the other side, 3 to 4 minutes. An instant-read thermometer inserted into the center should read 145 degrees F (63 degrees C). Do not overcook the chops or they will turn dry and hard.

Remove pork chops from heat and cover to keep warm.

Combine chicken broth, balsamic vinegar, and honey in a small saucepan. Bring glaze to a boil over medium-high heat and boil until mixture is reduced to 1/2 cup, 5 to 6 minutes.

Drizzle pan-fried chops with balsamic glaze and serve warm.