In a shallow dish, whisk together the flour, cornstarch, salt, and pepper.
In another shallow dish, whisk together the eggs and milk.
Dip each shrimp into the egg mixture, allowing any excess to drip off, then dredge it in the flour mixture, ensuring it's fully coated. Place coated shrimp on a plate.
Heat the vegetable oil in a large skillet or Dutch oven over medium-high heat to 350°F (175°C).
Carefully add shrimp to the hot oil in batches, being careful not to overcrowd the pan. Fry for 2-3 minutes per side, or until golden brown and cooked through.
Remove shrimp with a slotted spoon and drain on paper towels. Repeat with remaining shrimp.
Serve immediately with your favorite dipping sauce.
Notes
For an extra kick, add a pinch of cayenne pepper to the flour mixture. These are best served immediately for maximum crispiness.