BEAT butter in the bowl of a stand mixer fitted with the paddle attachment at medium speed until smooth, 1 to 2 minutes. Add confectioners’ sugar, granulated sugar, ground coffee, zest, and salt. Beat at medium-low speed until smooth, about 1 minute. Add egg yolk and vanilla. Beat until combined, about 1 minute.
SIFT flour, and lightly spoon into a measuring cup for 3 cups. With mixer on low speed, add flour mixture to butter mixture in two additions, beating until combined.
SHAPE dough into a 12×2-inch log. Wrap in plastic wrap and refrigerate until firm, at least 2 hours.
PREHEAT oven to 325°. Line 2 rimmed baking sheets with parchment paper.
CUT dough crosswise into ¼-inch-thick rounds using a serrated knife. Place at least 1 inch apart on prepared baking sheets.
BAKE until tops of cookies are set, and bottoms are lightly golden, 15 to 18 minutes. Let cool on pans for 1 minute; transfer to a wire rack and let cool completely.
MICROWAVE chocolate in a small bowl on high in 10-second intervals, stirring between each, until melted and smooth, 1 minute to 1½ minutes. Stir in shortening until smooth and well combined. Spoon chocolate into a small piping bag or resealable plastic bag; cut a ¼-inch hole in tip or corner.
DRIZZLE chocolate mixture over shortbread as desired. Let stand until set before serving, 15 to 20 minutes.