In a large mixing bowl, combine the well-drained canned tuna, chopped green onions, grated carrot, salt, and pepper. Crack in the eggs and sprinkle in the all-purpose flour, mixing until everything is evenly combined.

With your hands, take portions of the mixture and shape them into small patties, approximately 2–3 inches in diameter. Aim for about 8 patties total.

Heat a generous amount of oil in a non-stick skillet over medium heat. Once the oil shimmers, carefully add the formed patties in a single layer. Cook for about 2–3 minutes on each side until they are golden brown and crispy.

While the tuna cakes are sizzling, mix together mayonnaise, gochujang, lemon juice, and a pinch of sugar in a separate bowl. Whisk until smooth and creamy.

Once the patties are cooked, transfer them onto paper towels to drain any excess oil. Serve immediately, drizzled with the spicy mayo.