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For the sauce, add all ingredients, except for blue cheese, to a blender or food processor. Blend until smooth.
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Stir blue cheese in manually.
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If sauce is too thin for your liking, add a bit more sour cream and mayo (or blue cheese), and blend until incorporated.
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Pour into an airtight container and keep refrigerated until ready to serve.
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For the pickles, drain pickle juice from jar and lay pickle slices out on paper towels to dry.
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Line a baking sheet with several paper towels. Place a cooling rack over the top of the baking sheet and set aside.
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Heat 2 inches of oil in a big heavy bottomed pot (like an enameled cast iron dutch oven) over medium-high heat until oil is about 385 degrees F.
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In a medium mixing bowl, combine flour, Cajun seasoning, garlic powder, salt, black pepper, hot sauce and buttermilk and whisk to combine well. Mixture should be smooth. Mixture should be a thick pancake batter consistency. If too dry, add water a tablespoon at a time, until it reaches desired consistency.
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Place 5-6 pickle chips into the batter, turning to coat all sides. Shake off excess batter, then gently place into the hot oil.
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Fry pickles about 1-3 minutes per side, until golden brown on both sides.
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Carefully remove pickles from oil and place them on the cooling rack.
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Repeat with remaining pickles and peppers from the jar if you wish.
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Serve with blue cheese dip.