In a large bowl, combine drained tuna, chopped onion, grated carrot, and finely chopped green onion. Season with salt and pepper to taste. Add eggs and flour, mixing until combined.

Shape the mixture into 2-3 inch patties, yielding about 8 cakes; place on a parchment-lined plate.

Heat oil in a skillet over medium heat. Fry patties for 2-3 minutes on each side until golden brown.

In a separate bowl, whisk together mayonnaise, gochujang, lemon juice, and sugar until smooth to make the spicy mayo.

Serve the crispy tuna cakes hot, drizzled with spicy mayo or as a dipping sauce.