Open up chile and place on egg roll wrapper with corner facing you.
Place cheese stick on chile and roll up, tucking in corners and moistening edges to seal.
Toss in cornstarch, dusting liberally.
(Can be made up to this point a day ahead. Leave in cornstarch. Cover and refrigerate.) Shake off excess cornstarch and deep fry in 350 oil to cover until lightly golden and cheese just starts to ooze out.
Drain on paper towels and keep warm in 250 oven.
Serve as a side dish or appetizer with your favorite Mexican meal.