3-inch cookie cutters, disposable pastry bags and small decorating tips
For the dough: Whisk together the flour, baking soda and salt in a medium bowl. Beat together the egg and vanilla in a small bowl.
Beat together the butter, granulated sugar and confectioners' sugar in a large bowl with an electric mixer on low speed. Once incorporated, increase the speed to medium and beat until slightly creamy, about 3 minutes. Beat in the grapefruit zest and chopped basil until incorporated. Stop and scrape down the sides of the bowl as needed.
Reduce the speed to low, slowly pour in the egg mixture and beat until combined. Add the flour mixture, in 3 additions, increasing the speed as the dough gets thicker to keep the beaters spinning. Scrape down the sides of the bowl and the beaters themselves as needed. Once all the flour mixture is just incorporated, increase the speed to medium-high and beat until the dough is very smooth, about 5 minutes.
Turn the dough out of the bowl and bring it together. Divide into 2 equal pieces. Shape each piece into a flat square and wrap in plastic wrap. Refrigerate the dough at least 1 hour and up to overnight.
To roll, cut and bake the cookies: Position racks in the upper and lower thirds of the oven, and preheat to 350 degrees F. Line 2 baking sheets with parchment.
Dust another sheet of parchment paper with flour and put 1 piece of the dough on top. Dust with more flour and top with another sheet of parchment. Roll the dough out into a rectangle about 1/4-inch thick (about 11 x 9 inches) and place in the freezer for 5 minutes.
From 1 piece of rolled dough, cut out cookies with a 3-inch cutter and arrange cookies on the prepared baking sheets, about 2 inches apart. Refrigerate while you cut the remaining cookies. Reroll and cut any scraps of dough. If the dough becomes very soft and difficult to roll or cut at any point during the process, place on a baking sheet in the freezer for 5 minutes.
Bake, rotating the baking sheets front to back and bottom to top about halfway through, until golden brown around the edges, about 12 minutes. Let cool completely on the baking sheets on a cooling rack, about 30 minutes.
For the royal icing: Combine the confectioners' sugar and meringue powder in a large bowl. Add the grapefruit juice and beat with an electric mixer on medium-high speed until the icing forms thick and glossy peaks, about 2 minutes, adding more grapefruit juice, 1 teaspoon at a time, if needed.
Color icing as desired with gel food coloring. Fit pastry bags with small round tips and fill with the icing. Decorate the cookies as desired and let dry for 30 minutes.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)