Toss red onion and a pinch of salt in a small bowl to coat; let sit 5 minutes to allow onion to soften slightly. Rinse under running water, then shake off excess water. Place onion in a medium bowl and add cabbage, vinegar, and 2 tablespoons oil. Toss to combine and season slaw with salt and pepper.
Pound chicken thighs with a meat mallet or a rolling pin between 2 pieces of plastic wrap to 1/4″ thick. Place cornstarch in a shallow bowl. Whisk eggs, mustard, and cayenne in another shallow bowl.