Here’s a deliciously crisp and tender sugar cookie that can assume many shapes and be served as is, or sandwiched with jam, chocolate, or your favorite filling.

Position 1 oven rack in the top third of the oven and 1 oven rack in the bottom third of the oven, and preheat the oven to 350°F. Line 2 baking sheets with parchment paper.

Make the cookies. Put the butter and sugar in a large bowl. Using a mixer, beat on low speed for 1 minute. Turn up the speed to medium and beat for another minute. The mixture should be blended and smooth. Turn off the mixer. Using a silicone spatula, scrape down the sides of the bowl. Add the egg and vanilla and beat on medium-low speed until well blended. Turn off the mixer. Scrape down the sides of the bowl.

Put the flour and salt into a medium bowl and whisk until blended. Add the dry ingredients to the butter mixture and beat on low speed just until the ingredients are blended and no patches of flour are visible. The mixture will have the texture of gravel and pebbles. Scrape down the bowl one last time, and make sure no clumps of flour are hiding in the bottom.

Dump the clumps of dough onto your work surface, and squeeze them together until they form a cohesive dough. Flatten the dough into a 9-inch circle, wrap in plastic or parchment, and chill for 30 minutes before continuing.

Place a large sheet of parchment paper on your work surface, about the size of a baking sheet. Have a second parchment sheet the same size ready. Remove the dough from the refrigerator and place it in the center of the first parchment sheet. Top with the second parchment sheet, and flatten the dough slightly. Using a rolling pin, and starting from the edge closest to you, roll gently but firmly to the edge opposite you and then back again twice. Be careful not to roll the pin off the edge of the dough, or the dough will stick to the paper. Turn the dough, between the parchment paper, a quarter turn and roll up and back again twice. Repeat rolling up and back and turning until the dough is ¼ inch thick.

If the paper creases into the dough, gently peel back the paper, straighten it out, and smooth it back on top of the dough. You’ll need to do this several times during the rolling process. If the dough gets too soft and squishy while you are rolling, transfer it to a baking sheet (still between the parchment paper) and refrigerate for 10 to 15 minutes, until cool but flexible.

Peel off the top sheet of parchment. If the dough is soft and sticky, refrigerate for 15 minutes. Using the cookie cutters, press down firmly to cut out the shapes. Cut them as close together as possible. Using a small offset spatula, lift the shapes off the parchment paper and transfer to the prepared pans, spacing them about 1 inch apart. Press all the dough scraps together, roll the dough out, and cut out more shapes.

Place 1 baking sheet on each oven rack. Bake for 8 minutes, then, using oven mitts, switch the pans between the oven racks. Bake for another 5 to 9 minutes, until the cookies are golden brown around the edges and lightly golden in the center. Using oven mitts, transfer the pans to the cooling racks and let the cookies cool completely before decorating. You may need to reuse the pans to finish baking all the cookies. Let the pans cool before you put more dough on them for baking.

Make the icing. Sift the powdered sugar into another medium bowl. Put the meringue powder and water in a large bowl. Make sure the bowl and your mixer beaters are very clean so the icing will whip up nicely. Beat the meringue on medium speed for about 1 minute, then turn the mixer to high and continue to whip until the mixture looks like whipped cream and has formed soft peaks.

With the mixer on medium speed, add the sifted sugar, about ¼ cup at a time, shaking it gently over the bowl and letting it blend in slowly. Once all the s