01 - Combine chicken, black beans, corn, red bell pepper, red onion, cheese, cilantro, cumin, chili powder, smoked paprika, salt, pepper, and lime juice in a large mixing bowl. Mix until evenly distributed throughout the mixture.
02 - Position an egg roll wrapper on a clean surface with one corner pointing toward you in a diamond orientation. Place approximately 2 heaping tablespoons of filling on the lower third section of the wrapper.
03 - Fold the bottom corner up over the filling, then fold both side corners inward toward the center. Lightly brush the top corner with beaten egg and roll tightly upward to completely seal. Continue this process for 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, maintaining temperature throughout the frying process.
05 - Cook egg rolls in small batches without overcrowding the pan. Fry for 3 to 4 minutes, turning periodically to ensure even browning, until exterior becomes golden brown and crispy.
06 - Transfer cooked egg rolls using a slotted spoon or tongs to paper towels to drain excess oil. Allow to cool for several minutes before serving.
07 - Present alongside salsa, guacamole, or ranch dressing for dipping.