In bowl of electric mixer, combine butter and sugar. Beat on medium-high speed until light and fluffy, about 2-3 minutes. Blend in egg yolks one at a time, and vanilla extract. With mixer on low speed, add flour and salt until incorporated and a thick dough forms. Mix in cranberries and pistachios on low speed just until evenly incorporated.
Gather dough together and split into two even portions. Transfer each to a piece of parchment paper. Form into log about 1 3/4-inches in diameter. Roll dough tightly in parchment paper and twist the ends to seal. Transfer dough logs to freezer and chill until very firm, at least 2-3 hours.
To bake, preheat oven to 350?F. Line baking sheets with parchment paper or silicone baking mats. On piece of wax or parchment paper, pour a line of turbinado sugar for coating dough log. In small bowl, combine egg white and water. Remove dough from freezer, brush lightly with egg wash, and roll in turbinado sugar pressing gently to adhere. Transfer dough to cutting board and slice with a sharp knife into rounds just less than 1/2-inch thick. Place dough rounds on prepared baking sheets.
Bake until edges are light golden and cookies are just set, 14-15 minutes total. Let cool on baking sheets briefly, then transfer to a wire rack to cool completely.