Preheat oil to 350 degrees F in medium saucepan. Fill with enough oil that egg rolls will not rest on the bottom of pan. Mix egg and milk together, in a small bowl, for egg wash.
In medium saute pan over medium heat add olive oil, onion, and peppers. Sweat vegetables until slightly softened, about 2 minutes. Add roast beef and saute until onions are translucent, about 5 minutes more. Add cheese and mix thoroughly, until cheese begins to melt. Remove from heat, strain in a fine mesh sieve to remove excess moisture, and let cool.
Divide cooled mixture into 8 equal parts. Place mixture in center of each egg roll skin. Fold in side corners and roll, sealing edges with egg wash. Submerge egg rolls in oil and fry, making sure the rolls do not touch the sides or the bottom of the pan. Fry in batches, to avoid over-crowding. until golden brown. Remove egg rolls to paper towels to blot excess oil. Cut egg rolls on bias, place on a serving platter and serve hot.