In a stand mixer fitted with the paddle attachment, cream together butter and sugar on medium-high speed until light and fluffy, about 3 minutes. Add cream cheese and continue mixing, 2 minutes more, scraping down sides of bowl as necessary. Reduce speed to low and add flour, salt, and pepper. Mix until just incorporated.
Divide dough in half and form into two discs. Wrap tightly in plastic wrap and chill, at least 1 hour and up to overnight.
Meanwhile, in a medium bowl, stir together cocktail sauce, horseradish, lemon zest, and vodka and set aside.
Preheat oven to 350 degrees. Remove chilled dough from refrigerator and allow to temper, 15-30 minutes. Unwrap first disc and transfer to a lightly floured work surface. Lightly flour surface of dough and, using a floured rolling pin, roll out dough to an approximately 14” diameter circle. Using a 12” round cake pan or large bowl as a guide, trim edges of dough to form a neat circle. Repeat with remaining dough.
Divide cocktail sauce mixture between the two circles and spread into a thin layer over each. Scatter chopped parsley and celery leaves over each and sprinkle with celery salt. Using a pizza cutter, divide each circle into 16 wedges. Starting with the wide edge, roll each wedge into a crescent shape and transfer to two parchment-lined baking sheets, spacing about 2” apart. Transfer cookies to refrigerator and chill, 45 minutes to an hour.
In a small bowl, whisk together egg and 1 t. water. Remove cookies from refrigerator and brush lightly with egg wash. Sprinkle with additional celery salt and bake, rotating once halfway through, until golden, 25-30 minutes. Allow to cool slightly on baking sheets, 10 minutes, before transferring to a wire rack to cool completely.