In a large bowl, combine well-drained tuna, chopped onion, grated carrot, and minced green onion. Season with salt and pepper, then mix in beaten eggs and flour until evenly combined.

Shape the mixture into small patties, about 2-3 inches in diameter, forming around 8 cakes in total. Chill for 10 minutes to firm them up.

Heat a non-stick skillet over medium heat with oil. Fry the tuna cakes for 2-3 minutes on each side until golden brown and crispy.

While the cakes are cooking, whisk together mayonnaise, gochujang, lemon juice, and sugar until smooth.

Transfer cooked cakes to a paper towel to absorb excess oil. Serve warm with spicy mayo drizzled on top or on the side.