How to Make It
Place cornstarch in a large Ziploc bag. Line a baking sheet with parchment paper.
Whisk together eggs and milk in a shallow dish or bowl. Combine cornmeal, pepper, 1/2 cup Parmesan, and 1 teaspoon oregano in a separate shallow dish or bowl. Place cheese sticks in cornstarch, 5 at a time, shaking to coat. Remove from bag; tap off excess cornstarch. Dip cheese sticks in egg mixture, then dredge in cornmeal mixture, pressing to adhere. Place coated cheese sticks in a single layer on prepared baking sheet and freeze until firm, about 1 hour.
Pour oil to a depth of 2 inches into a Dutch oven or heavy bottom pot; heat over high to 375°F to 400°F. Fry cheese sticks, in batches, in hot oil until golden brown and crisp, about 2 minutes. Transfer to a plate lined with paper towels. Season with salt and a pinch each of Parmesan and oregano. Serve immediately with marinara sauce.