Season pork chops generously (as in, way more than you think!) with salt and pepper and allow to rest at room temperature for at least 30 minutes.
Heat a 10-inch skillet, preferably cast iron, over medium-high heat for several minutes. Add oil and warm for 30 seconds. Turn on your oven vent—things are about to get smoky! Cook pork chops for 3 minutes per side, or until an instant thermometer registers 135 degrees F. If the sides look pink, use tongs to sear each side for 30 seconds. Transfer pork chops to a holding plate and reduce heat to medium.
When the skillet has cooled for a few minutes, add the second tablespoon of oil, red onion, garlic, and thyme. Season with salt and pepper. Cook for about 5 minutes, stirring often, until the onions are soft but not totally shapeless. Add the plums and cook for 3 to 4 minutes, until they are soft and warm, but not mushy. Remove skillet from heat and stir in lime juice and butter until melted.
Return the pork chops and any juices that have collected on the plate to the skillet. Garnish with more thyme and serve straight from the skillet.