Unwrap 12 cheese sticks and cut them in half crosswise.
Combine flour, paprika, and salt in a Combine ½ cup flour, ⅛ teaspoon paprika, and ⅛ teaspoon salt in a gallon-sized resealable plastic bag.
In a second bag, mix 1½ cups panko, 1 tablespoon parsley, and 1 teaspoon oregano.
In a bowl, beat 2 eggs and ¼ cup milk.
Add 5 or 6 cheese sticks to the bowl with eggs and milk and toss around to coat. Transfer sticks to the flour bag and shake around, then return them to the milk bowl, making sure to coat every side.
Finally, add sticks to the panko bag and toss to coat. Place panko-coated sticks on a baking sheet. Repeat to coat all the remaining cheese sticks.
Place the baking sheet in the freezer for 20–30 minutes. This will ensure that the cheese does not ooze out of the coating while frying.
Heat a few inches of vegetable oil in a large frying pan to 350–375°F.
Working in batches, fry sticks in the oil until golden brown on all sides, 30–60 seconds. Drain on a paper towel–lined plate.
Make ahead of time. Bread your cheese sticks ahead of time and pop them in the freezer. Once they are frozen, transfer them to an airtight container or resealable plastic freezer bag. Store for up to 1 month before frying as instructed above.