Drain the canned tuna and transfer it to a mixing bowl.
Add the shredded carrot, cilantro, shredded red cabbage, lemon juice, and 1/4 cup mayonnaise to the tuna; season with salt and pepper and mix until combined.
Lay out bread slices and divide the tuna mixture among half of them.
Top the tuna on each sandwich with 2–3 slices of provolone, then place the second slice of bread on top.
Spread the remaining 2 tablespoons mayonnaise on the outside of both bread slices of each sandwich.
Preheat the waffle maker and place the assembled sandwich inside; cook until the bread is golden and crisp, about 3–5 minutes (time may vary by waffle maker).
Carefully remove the sandwich, let it rest 1 minute, then cut and serve.
