In a large mixing bowl, combine the well-drained canned tuna, chopped onion, grated carrot, and chopped green onion. Season with salt and pepper, add in the eggs, mixing thoroughly before incorporating the flour.

Take portions of the mixture and shape them into small patties about 2–3 inches in diameter.

Preheat a non-stick skillet over medium heat, add oil, and place the patties in a single layer. Cook for 2–3 minutes on each side until golden brown.

While the tuna cakes are cooking, whip up the spicy mayo by combining mayonnaise, gochujang, lemon juice, and sugar. Whisk until smooth.

Transfer the cooked tuna cakes to a paper towel-lined plate to absorb excess oil. Serve hot with spicy mayo.