01 - In a large mixing bowl, combine cooked chicken, black beans, corn, red bell pepper, red onion, Monterey Jack cheese, cilantro, ground cumin, chili powder, smoked paprika, kosher salt, black pepper, and fresh lime juice. Mix thoroughly until all ingredients are evenly distributed.
02 - Position an egg roll wrapper on a clean work surface with one corner facing you in a diamond orientation. Place approximately 2 heaping tablespoons of the filling mixture onto the lower third section of the wrapper.
03 - Fold the bottom corner up and over the filling. Fold both side corners inward toward the center. Brush the remaining top corner with beaten egg, then roll up tightly from bottom to top, pressing gently to seal the egg roll securely. Repeat this process with all remaining wrappers and filling.
04 - Pour vegetable oil into a deep skillet or fryer to a depth of 2 inches. Heat the oil to 350°F, monitoring the temperature carefully with a kitchen thermometer for accurate results.
05 - Fry the egg rolls in small batches to avoid overcrowding the pan, which would lower the oil temperature. Cook for 3 to 4 minutes, turning occasionally with tongs or a slotted spoon, until golden brown and crispy on all sides.
06 - Transfer the cooked egg rolls to a plate lined with paper towels to drain excess oil. Allow them to cool for a few minutes before serving to prevent burns and let the filling set slightly.
07 - Arrange the egg rolls on a serving platter and serve immediately while hot and crispy. Accompany with salsa, guacamole, or ranch dressing for dipping as desired.