In a large mixing bowl, combine the well-drained canned tuna, chopped onion, grated carrot, and sliced green onion. Season with salt and pepper to taste, then crack in the eggs and sprinkle the all-purpose flour. Gently fold the mixture together until just combined.

Using your hands, take portions of the mixture and shape them into small patties about 2-3 inches in diameter. Carefully place the patties on a tray lined with parchment paper.

Heat cooking oil in a skillet over medium heat. Once shimmery, gently place the patties into the pan. Cook for 2-3 minutes on each side until golden brown and crispy.

While the tuna cakes are frying, whip up the spicy mayo. In a separate bowl, combine mayonnaise, gochujang, lemon juice, and sugar if desired. Whisk until smooth.

Once cooked, transfer patties to a plate lined with paper towels to drain excess oil. Serve warm with spicy mayo.