Add ice water, granulated sugar and 1 teaspoon salt to a medium bowl. Mix until sugar and salt have dissolved.
Add shrimp. Set aside 15 minutes, then drain well and pat dry.
Place shrimp in a another, dry bowl. Add 1/2 teaspoon Cajun seasoning. Toss to coat.
In another, large bowl, add flour, cornstarch, confectioners' sugar, remaining 1 1/2 teaspoons Cajun seasoning and beer. Whisk to make a smooth batter.
Add the shrimp, pepperoncini and roasted peppers to batter. Stir until evenly coated. Set aside.
Heat 2 inches of vegetable oil in a Dutch oven or large cooking pot over medium-high heat until a deep fry thermometer registers 350°F.
Working in batches, remove shrimp, pepperoncini and roasted peppers from the batter with a slotted spoon. Transfer to the hot oil. Fry until golden, about 3 minutes.
Remove a clean slotted spoon or a spider-strainer and place on a paper towel-covered plate to drain.
Continue in batches until all shrimp, pepperoncini and roasted peppers are cooked.
Season with salt and pepper, to taste.
Serve with lemon wedges, cocktail sauce and/or tartar sauce.