In a large mixing bowl, combine the drained canned tuna, chopped onion, grated carrot, and chopped green onion. Add a pinch of salt and pepper to taste, followed by the two beaten eggs and flour. Stir until everything is well incorporated, forming a cohesive mixture that holds together.

Using your hands, scoop out portions of the tuna mixture and shape them into patties about 2–3 inches wide. Aim for a uniform thickness to ensure even cooking. You should yield around eight cakes. Place them on a plate, ready to be cooked.

Heat a generous amount of oil in a non-stick skillet over medium heat. After about 2 minutes, carefully place the tuna cakes in the skillet, ensuring they don’t overcrowd the pan. Cook for 2–3 minutes on each side until they are golden brown and crispy. Keep an eye on them, adjusting the heat if necessary to avoid burning.

While your patties are sizzling, prepare the spicy mayo. In a separate bowl, mix together mayonnaise, gochujang, lemon juice, and sugar until you achieve a smooth and creamy consistency. Taste and adjust the seasoning based on your preference for spice and sweetness.

Once the tuna cakes are perfectly golden, transfer them to a paper towel-lined plate to absorb any excess oil. Serve them warm on a platter, drizzled with your homemade spicy mayo or served on the side for dipping.