In food processor or mixer blend cheddar cheese, cream cheese and butter until smooth. Add flour, salt, paprika and cayenne; mix until just combined. Roll dough into a 12-inch log. Wrap in waxed paper and chill for one hour.
Cut roll into 1-inch pieces and roll each piece into a 12-inch rope on lightly floured surface. Transfer ropes to waxed paper. Lightly beat egg with water; brush dough with egg mixture; roll in Parmesan cheese that has been spread out on waxed paper.
Form ropes into pretzels, pressing ends down lightly to secure them. Arrange pretzels on a baking sheet lined with parchment paper and chill for one hour. Bake at 375 degrees for 12–15 minutes until golden. Leave on baking sheet for two minutes and then transfer to rack to cool. Makes 12 pretzels.
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