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 combined.
02 - Place an egg roll wrapper on a clean work surface with a corner pointing toward you. Spoon about 1 tablespoon of the filling onto the lower third of the wrapper.
03 - Fold the bottom corner over the filling, then fold in the sides and roll up tightly. Brush the top corner with beaten egg to seal. Repeat with remaining wrappers and filling.
04 - Heat 2 inches of vegetable oil in a deep skillet or Dutch oven to 350°F.
05 - Fry the egg rolls in batches, turning occasionally, until golden brown and crispy, about 2–3 minutes per batch. Do not overcrowd the pan.
06 - Remove egg rolls with a slotted spoon and drain on paper towels. Serve warm, optionally with ranch or your favorite dipping sauce.