How to Make It
Whisk together the flour, 3 tablespoons poppy seeds, salt, and cloves in a medium bowl; set aside.
Beat the butter, granulated sugar, ⅓ cup confectioners’ sugar, and grapefruit zest with an electric mixer on medium-high until light and fluffy, 2 to 3 minutes. Add the egg yolk and vanilla and beat to combine. Reduce the mixer speed to low, gradually add the flour mixture, and mix just until combined (do not overmix). Chill for at least 2 hours and up to 3 days.
Heat oven to 350° F with the racks in the upper and lower thirds. Line 2 large rimmed baking sheets with parchment. In a small bowl, whisk together 1 cup confectioners’ sugar with the grapefruit juice.
Roll level tablespoonfuls of the dough into balls. Place the balls on the prepared baking sheets, spacing them 1 inch apart.
Bake, rotating the baking sheets halfway through, until the edges are lightly golden and firm to the touch, 12 to 14 minutes. Cool slightly on the baking sheets, then dip the warm cookies in the glaze. Immediately sprinkle with the remaining 1 tablespoon of poppy seeds and 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.