Dredge the mozzarella sticks: Spread the flour and breadcrumbs on separate plates (pie plates work well for this). Add the Italian seasoning, salt and pepper to the breadcrumbs and mix well. Place the eggs in a small bowl and beat them lightly.
Drop a piece of cheese into the flour and roll it around until it is well covered. Shake off the excess flour and dip the cheese into the egg mixture before rolling it in the breadcrumbs until well coated. One last time, dip the breadcrumb coated cheese back into the beaten egg and roll again in breadcrumbs to create an extra crispy coating. Set aside on a clean plate and repeat with the remaining cheese sticks. Once all of the mozzarella has been breaded, place the plate into the freezer uncovered and freeze until the breadcrumb coating is firm, at least 2 hours.
Meanwhile, make the buttermilk dip: In a small bowl, whisk all of the ingredients together until well combined. Cover with plastic wrap and refrigerate until ready to serve.
Fry the mozzarella sticks: Pour enough oil into a large heavy-bottomed pot to come to a depth of at least 2 inches. Using an candy thermometer, heat oil until it reaches a temperature of 350°. Fry the mozzarella sticks in batches, being careful not to overwhelm the oil, until crispy and browned on the exterior, about 5 minutes. Drain on paper towels.
Repeat with remaining mozzarella, allowing the oil temperature to rise back to 350° between batches. You can place the finished mozzarella sticks in a 200° oven to keep them warm while the others fry.
Serve immediately with buttermilk dip.