Make the cookies: In a small pot cook the butter over medium-high heat, stirring frequently, until golden brown, 6 to 7 minutes. Transfer the butter to a small bowl and chill until firm, 1 to 2 hours. Whisk together the flour and salt, in a medium bowl; set aside.
In a separate bowl, beat the chilled butter, brown sugar, granulated sugar, and orange zest with an electric mixer on medium-high until light and fluffy, 2 to 3 minutes. Add the vanilla and 1 of the egg yolks and beat to combine. Reduce the mixer speed to low and gradually add the flour mixture, mixing just until combined (do not overmix).
Form the dough into a 1½-inch diameter log. Wrap tightly in plastic wrap and refrigerate until firm, at least 2 hours or up to 3 days. (The dough can be frozen at this point for up to 2 months).
Heat oven to 350° F. Line two baking sheets with parchment. Unwrap the dough and cut into ½-inch slices with a serrated knife; place on the prepared baking sheets, spacing them 2-inches apart. Brush with the remaining egg yolk and sprinkle with the turbinado sugar.
Bake until the edges are lightly golden and firm to the touch, 11 to 13 minutes. Cool slightly on the baking sheets, then transfer to a wire rack to cool completely.
Storage suggestion: Keep the cookies at room temperature in an airtight container for up to 5 days.
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