Mix 3 cups ice water, the granulated sugar and 1 teaspoon salt in a medium bowl. Add the shrimp and set aside 15 minutes, then drain well and pat dry. Dry the bowl; return the shrimp to the bowl and toss with 1/2 teaspoon Cajun seasoning.
Whisk the flour, cornstarch, confectioners' sugar, the remaining 1 1/2 teaspoons Cajun seasoning and the beer in a large bowl to make a smooth batter. Add the shrimp, pepperoncini and roasted peppers and stir until evenly coated.
Heat 2 inches of vegetable oil in a Dutch oven over medium-high heat until a deep-fry thermometer registers 350 degrees F. Working in batches, remove the shrimp, pepperoncini and roasted peppers from the batter with a slotted spoon, transfer to the hot oil and fry until golden, about 3 minutes. Remove and drain on paper towels; season with salt. Serve with lemon wedges, cocktail sauce and/or tartar sauce.