Prepare the tuna mixture by combining well-drained canned tuna, finely chopped onion, grated carrot, and sliced green onion in a large mixing bowl. Season with salt and pepper, add eggs and flour, and mix until well combined.

Shape the mixture into small patties, about 2-3 inches in diameter. Aim for 8 equal-sized cakes and place them on a plate lined with parchment paper.

Heat oil in a non-stick skillet over medium heat. Once hot, carefully add tuna cakes in a single layer. Cook for 2-3 minutes on each side until golden brown and crispy.

While the patties are frying, mix together mayonnaise, gochujang, lemon juice, and sugar in a small bowl until smooth.

Once cooked, transfer patties to a paper towel-lined plate. Serve warm with spicy mayo drizzled on top or as a dipping sauce.