In a pan, melt unsalted butter over medium heat. Toss in the kimchi and saute for 1 to 2 minutes. Add rice and break it up using a spatula then mix well.
Season the rice with kimchi juice, soy sauce, gochujang, and sesame oil. Add the parmesan cheese and stir to mix well.
Stir fry for another 1 to 2 minutes. Transfer the rice to a bowl and set aside to cool completely.
Once the rice has cooled to the touch, grab about 2 tablespoons of fried rice onto your hand. Flatten it out into a disk then place 1 tablespoon of shredded mozzarella cheese in the center. Cover with another 2 tablespoons of fried rice then form into a ball. Make sure to squeeze the fried rice balls with the palms of both hands so they stick together.*You can make the balls in advance and store them in the fridge until ready to fry. Next, prepare your fry coating stations. In a shallow plate or bowl, mix together all-purpose flour and 1/2 teaspoon salt. In a separate shallow plate or bowl, crack the eggs and whisk until homogenous. In another shallow plate or bowl, mix together panko breadcrumbs and 1/2 tsp salt.
Coat the kimchi rice ball in the flour then into the egg, making sure all sides are evenly coated. Transfer it to the panko breadcrumbs and gently press the breadcrumbs into the kimchi rice ball so it adheres better.
In a deep pot or pan, fill it up halfway with neutral oil. Heat to 375F or 190C. Carefully place the rice balls into the hot oil. I recommend working in batches to prevent the pot from overcrowding. Fry for 3 minutes or until golden brown and crispy.
Transfer to a wire rack to cool. Serve with Kimchi Mayo Sauce and garnishes. Enjoy!