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 well incorporated.
02 - Position an egg roll wrapper on a clean surface with one corner pointing toward you. Place approximately 1 tablespoon of filling onto the lower third of the wrapper.
03 - Fold the bottom corner over the filling, fold in both sides, then roll tightly upward. Brush the final corner with beaten egg to seal. 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 batches, turning occasionally, until golden brown and crispy, approximately 2–3 minutes per batch. Avoid overcrowding the pan.
06 - Transfer egg rolls to a paper towel-lined plate using a slotted spoon. Serve warm with ranch or preferred dipping sauce.