In a large bowl, combine the drained canned tuna, chopped onion, grated carrot, and green onion. Season with salt and pepper. Add in the beaten eggs and flour, mixing gently until just combined.

Using your hands, form the mixture into patties about 2-3 inches in diameter, making around 8 pieces. Set aside and preheat your skillet.

In a non-stick skillet, heat enough oil over medium heat. Once shimmering, place the tuna patties carefully in the skillet. Cook for about 2-3 minutes on each side until golden brown.

While the tuna cakes are cooking, mix together mayonnaise, gochujang, lemon juice, and sugar in a small bowl until smooth. Adjust spice level as desired.

Once cooked, transfer tuna cakes to a paper towel-lined plate. Serve warm drizzled with spicy mayo or with a small bowl for dipping.