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 fully incorporated.
02 - Position an egg roll wrapper with a 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 the sides, and roll tightly. Seal the final corner with beaten egg. 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 - Remove with a slotted spoon and drain on paper towels. Serve warm with ranch or preferred dipping sauce.