2 sticks unsalted butter, at room temperature
1 large egg yolk
2 tablespoons plus 1/2 teaspoon finely grated pink grapefruit zest (from 2 large grapefruits)
1/2 teaspoon salt
2 cups confectioners' sugar
2 cups all-purpose flour, plus more for dusting
1 to 2 tablespoons fresh pink grapefruit juice
Red food coloring
Coarse sugar, for decorating
Position racks in the upper and lower thirds of the oven and preheat to 350 degrees F. Beat the butter, egg yolk, 2 tablespoons grapefruit zest and the salt in a large bowl with a mixer on medium speed until light and creamy, about 3 minutes. Add 1 cup confectioners' sugar and beat until combined. Reduce the mixer speed to medium low and gradually beat in the flour until incorporated.
Turn the dough out onto a lightly floured surface and dust with flour. Gently knead a few times until soft but not sticky, dusting the surface with more flour as needed. Roll out to slightly thicker than 1/4 inch thick and cut out circles with a 2-to-2 1/2-inch-round cookie cutter. Gather the scraps and reroll to cut out more cookies.
Arrange the cookies 2 inches apart on 2 baking sheets. Bake, switching the pans halfway through, until the cookies are firm and golden brown on the bottoms, 15 to 18 minutes. Let cool 5 minutes on the baking sheets, then transfer to racks to cool completely.
Whisk the remaining 1 cup confectioners' sugar, 1 tablespoon grapefruit juice and the remaining 1/2 teaspoon zest in a bowl until smooth. Gradually whisk in up to 1 tablespoon more grapefruit juice until the glaze is spreadable. Tint pink with food coloring. Spread about 1/2 teaspoon glaze on each cookie. Sprinkle with coarse sugar.
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