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.
Photograph by Levi Brown
Courtesy of Food Network Magazine