Preheat oven to 425°F. Prepare a large baking sheet by lining with tinfoil or parchment paper.
Heat oil on a large nonstick skillet over medium heat. When hot, add in minced garlic and ginger and sauté until aromatic, around 1 minute. Add in corn kernels and optional chopped kimchi. Cook until some moisture is released, especially if corn was frozen, around 3-4 minutes. Add in cabbage and green onion and cook until just wilted, around 3 minutes more. Remove from heat and stir in soy sauce, sesame oil, and salt and pepper to taste. Let cool completely.
Place an egg roll wrapper on a clean work surface. Add ¼ cup of corn filling onto the bottom third of the wrapper. Top with a small handful of grated cheese. Like rolling up a burrito, fold the bottom corner over the filling and tuck underneath. Roll tightly towards the center then fold in the sides. Keep rolling and brush the edge with water to seal. Place on prepared baking sheet. Repeat for all wrappers.
Using a pastry or silicone brush, brush all sides of egg rolls with oil. Bake in preheated oven for 20-25 minutes, flipping halfway through. If you prefer more browning, raise oven temperature to 450°F for the last 10 minutes of baking. Garnish with scallions and serve hot with gochujang dipping sauce.