Preheat the oven to 375 degrees.
Add the sliced steak to a bowl with the soy sauce, rice wine, ketchup, and brown sugar. Marinade for 30 minutes or up to 4 hours.
Pico de gallo: Mix all ingredients in a bowl. Season with salt and pepper to taste and set aside.
Kimchi: Place the cabbage and salt in a bowl, using your hands rub the salt and cabbage together until the cabbage softens and the moisture is drawn out. Then fill the bowl with cold water and let sit for 35 minutes. Drain the water and mix in the remaining ingredients until well combined. Taste and adjust any of the ingredients as needed. (Use more or less sriracha depending upon your desired level of spiciness). Season with salt if needed and set aside.
For the beef: Drain the beef well. Heat a nonstick pan on medium high heat. Once the pan is very hot add the oil and the beef. Saute for 2 to 3 minutes until the beef is nicely browned. Then remove from the pan and set aside.
Layer the burrito with some cheese, kimchi, beef, more cheese, and pico. Fold in the ends and roll up tightly. Place on a baking sheet seam side down and into the oven until the cheese is melted, about 6 to 8 minutes.
Cut in half and serve.