Mash the avocado and combine it with the salt, pepper and mayonnaise. Make sure it's mashed properly and very creamy. The smoother it is, the easier it'll be to spread over the cucumbers.
With a vegetable peeler, thinly peel the cucumbers.
Put some saran wrap over a cutting board. Arrange 8-10 cucumber slices slightly overlapping each other horizontally over the wrap. Put another layer of cucumber slices vertically so that it covers the horizontally ones perfectly.
With a spoon or spatula, carefully spread some of the avocado cream over all of the cucumber slices. *If you do not put the cream over the cucumber slices, the filling tends to fall out of the sushi when cut. This cream helps the fillings stick together*
Line up vertically all of your preferred fillings on the right or left side. This could be sliced fish like salmon or tuna, cucumber or carrot sticks, cream cheese, onions, avocado, etc. You can also put some wasabi in there if you like your sushi spicy.
Turn the cutting board 90 degrees so that the filling is facing you and you will roll it forward. With the help of the saran wrap, pick up the cucumber sushi and slowly roll it forward applying a bit of pressure. This is compressing the sushi so that it holds its shape.
Once rolled, carefully remove the saran wrap around and slice the sushi into even pieces.