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Using an electric hand mixer, beat butter and blue cheese in a large bowl until combined and fluffy. (Or use a stand mixer fitted with the flat beater).
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Whisk together flour, salt, cayenne pepper, and red pepper flakes in a medium bowl. Add to the butter/cheese mixture and mix until crumbly, about 1 minute. Add 1 tablespoon water and mix until combined.
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Dump the dough onto a work surface and press it together tightly until it comes together in a ball. Roll dough into a log 2 inches thick by 10 inches long. Roll up the log with parchment or wax paper. Chill dough thoroughly, at least 4 hours or overnight.
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Preheat the oven to 350 degrees F. Line baking sheets with parchment or non-stick liner.
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Beat the egg with 1 tablespoon of water to make an egg wash. Un-roll the log from the parchment and brush dough with egg wash.
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Spread the chopped walnuts on the parchment paper and roll the log over the nuts to coat it evenly.
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Cut the log into 1/3-inch slices. Place cookies 1 inch apart on baking sheets and chill for 20 minutes.
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Bake for 18 minutes, or until lightly browned. Rotate baking sheet once during baking.
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Cook cookies on the baking sheet for 1 minute then transfer to a cooling rack. Cool completely.