Pat the pork chops dry and season both sides with salt, pepper, and thyme.
Heat the oil and 1 tablespoon of butter in a large skillet over medium-high heat. Add the pork chops and sear for 3 to 4 minutes per side until browned. Remove them to a plate.
Reduce the heat to medium and add the remaining 2 tablespoons of butter to the skillet. Add the sliced onions and cook, stirring often, for 20 to 25 minutes until they turn deep golden brown and caramelized.
Sprinkle the flour over the onions and stir for 1 minute to cook out the raw taste.
Slowly whisk in the beef broth, scraping up any browned bits from the bottom of the pan. Simmer for 3 to 4 minutes until the gravy thickens.
Return the pork chops to the skillet, spoon the onion gravy over the top, and simmer gently for 5 minutes until the chops are cooked through.