Open your egg roll wrapper package and lay the stack of wrappers on a large cutting board or clean counter. Cover them with a clean towel.
Fill a ramekin or small bowl with water and set that near your egg roll wrappers. Take one egg roll wrapper out from under the towel and lay it out on the cutting board in a diamond shape.
One point should be aiming toward your stomach making the egg roll wrapper a diamond shape. In the center of the egg roll wrapper, arrange four slices of pepperoni in an overlapping line and top with an unwrapped cheese stick.
Dip your finger into the water and use it to moisten the top two edges of the egg roll wrapper. Fold the bottom corner up and over the pepperoni and cheese and use the wrapper to gently snug the contents together.
Fold the corners in from either side and tuck them around the filling, then roll away from you toward the moistened edges. Press to seal.
If the corner has trouble sticking, you can re-moisten it and press again. If your egg roll wrappers continue to have trouble sticking, you can beat an egg and brush that on to seal them.
Set the wrapped pizza log on a plate or half sheet pan. Continue with the remaining egg roll wrappers, pepperoni slices, and mozzarella sticks, leaving a little space between the rolls so they will not stick together.