Preheat oven to 400°. Line a baking sheet with parchment. In a medium bowl, lightly beat egg. Add beef, onion, Parmesan, provolone, garlic, parsley, bread crumbs, basil, oregano, salt, and pepper. Gently mix to combine.
Portion out 1/2-ounce balls (about 2 teaspoons) of beef mixture (you should have about 36 total). Arrange balls on prepared sheet.
Bake meatballs until browned, about 10 minutes. Let cool 5 minutes.
Transfer meatballs to a large bowl. Add 1/2 cup marinara sauce and toss to coat.
With one corner of an egg roll wrapper facing you, sprinkle 1/4 cup mozzarella into the center of the wrapper, then arrange 4 meatballs on top, leaving a 1" border. Brush edges of wrapper with water, fold bottom corner up and over filling, then fold in the sides. Tightly tucking as you go, finish rolling wrapper away from you. Repeat with remaining filling and wrappers.
Into a large Dutch oven or other heavy pot fitted with a deep-fry thermometer, pour oil to a depth of about 2 1/2". Heat oil over medium-high heat until thermometer registers 350°.
Fry egg rolls, turning occasionally, until golden brown and crispy, 7 to 8 minutes. Transfer to a wire rack set inside a baking sheet to drain.
Arrange egg rolls on a platter. Serve with remaining 1 cup marinara sauce alongside.