Mash the avocados in a bowl, and mix in the sun-dried tomatoes, cilantro, Monterey Jack cheese, and a pinch of salt.
Lay an egg roll wrapper on a flat surface.
Place a generous spoonful of the avocado mixture in the center.
Brush the beaten egg along the edges of the wrapper, and fold the wrapper over the filling, rolling it tightly.
Seal the edges by pressing them firmly.
Repeat with the remaining wrappers and filling.
In a skillet, heat about two inches of vegetable oil over medium-high heat until hot.
Gently add the egg rolls, frying until golden brown on all sides.
Drain on paper towels to remove excess oil.
Serve warm, perhaps with a dipping sauce of your choice—ranch dressing complements it well.