In a heavy skillet begin to brown ground beef in 1 tablespoon oil. Add onion, green pepper, garlic, jalapeno(s), salt, chili powder, cumin and oregano. Stir to combine and continue to stir until onion and pepper begin to soften; drain well.
Add water, cover and reduce heat. Continue to cook until dry, approximately 25 minutes. Remove from heat and stir in grated cheese and Tabasco sauce.
Lay out all 24 egg roll skins flat with points facing you (like a diamond). Place 1 heaping tablespoon of meat and cheese mixture in center of each skin.
Fold bottom point of skin up to cover meat mixture. Fold left and right points into the center. Lastly, fold top point down to form a roll. Brush on beaten egg whites to seal.
Heat oil in deep fryer to 350ΒΊ F. Cook rolls a few at a time in the fryer until brown (approximately 1 minute). Drain on paper towels.
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