Preheat oven to 400 degrees. \nPlace the onion slices in a small bowl of ice-cold water. Let sit while you prepare the rest of your ingredients (this will help remove some of the bitter flavor from the onions). \nToss sweet potatoes with a drizzle of olive oil and a pinch of kosher salt. Place on a baking sheet and roast, flipping halfway through, until tender, about 20-25 minutes.\nIn a small bowl, whisk ¼ cup mayonnaise with the Korea sauce. \nOnce the onions have been sitting for at least 10 minutes, drain and pat to dry. Liberally coat one side of each slice of bread with Korea-spiced mayo. Layer the cheese, apple, sweet potato, arugula and onions between 2 slices of bread and sandwich together.\nSpread the reserved 2 Tbsp mayonnaise on the outside of the sandwiches (this will help your grilled cheese get nice and crispy!). \nHeat a large skillet over medium heat and add the butter. Once the butter has melted, place the sandwiches (working one at a time, if necessary), mayo side down, into the pan. Press down on the sandwiches with a spatula and grill until golden brown on the bottom side, about 3-5 minutes.\nFlip over and continue cooking until well-browned on both sides and the cheese has melted, about 3 minutes more. Slice and serve immediately, with any extra Korea-spiced mayo for dipping!