In a large bowl, combine the drained tuna, finely chopped onion, shredded carrot, and sliced green onion. Season with salt and black pepper to taste. Add the eggs and all-purpose flour, mixing well until everything is fully integrated. The mixture should hold together without being too wet. Set aside for a moment to allow the flavors to meld.

With lightly oiled hands, scoop the mixture and shape it into patties about 2–3 inches in diameter. Ensure each patty is compact to maintain its shape while cooking.

Heat 2 tablespoons of neutral cooking oil in a non-stick skillet over medium heat. Once the oil is shimmering, carefully add the patties in a single layer. Cook each patty for 2–3 minutes on one side, or until they are golden brown and crispy.

While the patties are cooking, prepare the spicy mayo. In a small bowl, combine mayonnaise, gochujang, fresh lemon juice, and optional sugar. Stir until the mixture is smooth and creamy.

Once cooked, transfer the tuna cakes to a paper towel-lined plate to drain any excess oil. Serve the cakes warm, drizzled with the spicy mayo or as a dip alongside.