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