Combine the cabbage and cucumbers in a colander. Add the sea salt; and mix well. Place the colander over a bowl and let drain, until slightly wilted.
Meanwhile, season pork generously with salt, then rub with 1 tablespoon oil. Heat a dry medium skillet, preferably cast iron, over medium. Add pork chops and sear until deeply browned, 5–9 minutes on each side. Add sliced garlic and butter to skillet and swirl to melt butter. Tilt pan toward you so butter pools and spoon foaming butter over chops until butter is browned, about 1 minute. Transfer pork chops to a cutting board and let meat rest while you make the salad.
Combine the rice vinegar, honey, chili paste, grated ginger and minced garlic in a large bowl and stir. Shake the moisture from the cabbage and cucumber. Add to bowl and toss well to combine. Serve pork chops with spicy cabbage salad.