Combine cracker crumbs, flour, salt, and peppers in a large mixing bowl; taste and adjust seasoning as desired.

Place buttermilk and egg in another mixing bowl; whisk to combine.

Plac a large Dutch oven over high heat; pour cooking oil to 2 inches deep. Heat oil to 360˚F.

Add shrimp to egg wash; stire. Using a slotted spoon, working in batches, scoop shrimp from egg wash and toss in cracker crumb mixture. Carefully transfer to hot oil and fry until golden, 2 to 4 minutes. Using a slotted spatula or skimmer, transfer to paper towels to drain; repeat until all shrimp are fried. Serve at once with your favorite tartar sauce, cocktail sauce, or remoulade.