Cut the crust off each slice of bread. Using a rolling pin, roll out as thin as possible.
Place the long side of the rolled-out bread closest to you.
Thinly spread 1/3 of the tuna onto 1/3 of the bread, lengthwise.
On top of the tuna, arrange a few carrot, cucumber, and pepper strips, making sure not to overstuff the roll (a little goes a long way).
Starting with the side closest to you (the filled end), roll the bread tightly and press to seal into a roll. (If necessary, dab a little mayonnaise across the end of the roll to act as a glue and seal the roll.)
Cut the roll into 4 even slices and repeat with the remaining bread and tuna. Serve, cut side up, like sushi rolls.