Place the white vinegar, water, agave nectar, mustard seeds, and salt in a small saucepan and bring to a boil over high heat. Add the sliced red onion and stir to coat. After 60 seconds, turn off the heat and let the onions sit in the hot brine for 10 minutes. Transfer everything to a container or jar and refrigerate until fully cooled.
Place the gochujang, agave nectar, apple cider vinegar, and orange juice in a small saucepan. Warm over medium heat, stirring constantly with a whisk. After 2–3 minutes, when the mixture is hot and fully loosened, remove from heat and whisk until smooth. Set aside.
For the sriracha mayo, place all ingredients in a small bowl. Whisk until completely smooth and emulsified. Set aside.
To make the seitan, warm the canola oil in a large frying pan over medium-high heat. In a mixing bowl, combine ½ cup of the all-purpose flour with gochugaru and sesame seeds. In a separate bowl, whisk together the plant-based milk, sriracha, and remaining 2 tablespoons all-purpose flour until smooth.
Coat each piece of seitan in the flour mixture, then dip into the wet mixture, allowing excess to drip off. Immediately return each piece to the flour mixture for a second coating.
After 90 seconds when the oil is hot, carefully place the coated seitan into the pan. Fry for 3 minutes per side until golden brown and crisp. Transfer to a wire rack to drain.
Heat a skillet over medium-high heat. Place the buns cut side down on the dry pan and toast for 2–3 minutes until golden brown.
Spread sriracha mayo on the top and bottom buns. Place arugula on the bottom buns.
Warm the prepared sauce in the same pan over medium heat for 1–2 minutes, then add the fried seitan cutlets and coat evenly to glaze.
Place the sauced seitan over the arugula. Top with kimchi and pickled onions. Close the sandwiches and serve immediately.