Dice the ahi into 1/2 inch cubes and mix with the mayo. Refrigerate until ready to use.
Have a small bowl of water on the side before you begin building the burritos. Lay one sheet of nori on a work surface. Dip your hand in the water and use it to scoop a handful of rice. Spread an even layer of rice over the nori leaving a one inch strip bare at the back. If the rice begins sticking to your hand, dip it back in the water and continue spreading the rice. Top the rice with 3 ounces of ahi and 1/4 of the veggies. Drizzle on the unagi sauce and sprinkle with sesame seeds.
Dab a little water on the exposed nori. Starting at the end closest to you, roll up the sushi. The damp nori should seal the roll together. Allow to stand for 1-2 minutes before slicing. Continue rolling the sushi until all of the burritos have been made. Slice in half and serve.