Arrange stack of egg roll wrappers on a clean work surface in front of you like a diamond. Working with one at a time, brush surface lightly with water. Place a mozzarella log across bottom third of diamond. Roll cheese up tightly in wrapper, tucking corners in halfway through. Seal edges, then repeat with remaining wrappers and cheese.
Pour oil into a large nonstick skillet to come 1/8″ up sides; heat over medium-high until shimmering. Working in batches, fry mozzarella sticks, turning once, until golden brown, about 2 minutes per side. Transfer to paper towels and season immediately with salt. Let cool slightly before serving.