In a large bowl, whisk together the soy sauce, rice vinegar, sugar, gochujang, gochugaru, garlic, ginger, and sesame oil.
Add the chicken pieces and toss until fully coated. Let the chicken marinate for at least 15 minutes, or up to 1 hour if you have extra time.
Heat a large skillet over medium-high heat.
Add the marinated chicken and cook for 8–10 minutes, stirring occasionally, until the chicken is cooked through and slightly caramelized around the edges.
Reduce the heat to low and spread the chicken into an even layer in the skillet.
Sprinkle the mozzarella over the top, cover the skillet, and let the cheese melt until gooey.
Top with green onions and sesame seeds, then serve hot with rice.