01 - Combine cream cheese, cheddar, Monterey Jack, diced jalapeños, green onions, garlic powder, paprika, salt, and pepper in a medium bowl. Mix until smooth and thoroughly combined.
02 - Position an egg roll wrapper on a clean surface with one corner facing you. Place approximately 1 tablespoon of filling on the lower third of the wrapper.
03 - Fold the bottom corner over the filling, fold in both sides, and roll tightly. Brush the final corner with beaten egg to seal securely. Repeat with remaining wrappers and filling.
04 - Pour 2 inches of vegetable oil into a deep skillet or Dutch oven. Heat to 350°F.
05 - Fry egg rolls in small batches, turning occasionally, until golden brown and crispy, approximately 2-3 minutes per batch. Avoid overcrowding the pan.
06 - Remove egg rolls with a slotted spoon and drain on paper towels. Serve warm with ranch or preferred dipping sauce.