2cups (4 sticks)unsalted butter,at room temperature
3cupsgranulated white sugar
5cupsall purpose flour,plus more for dusting
ROYAL ICING (makes 2½ cups):
liquid or gel paste food coloring(optional)
PREPARE THE COOKIES:
In a large bowl, use an electric mixer to beat the butter and sugar on medium-high speed until light and fluffy, about 5 minutes. Add the eggs, vanilla, and salt; mix on medium-high speed until combined. With the mixer on low speed, add the flour in two batches, mixing until just incorporated.
Turn out the dough onto a clean work surface. Divide it in half, and pat into flattened rectangles; wrap each in plastic. Refrigerate for at least 2 hours or up to 1 week.
Preheat oven to 350°F., with rack in upper and lower thirds. Line large baking sheets with parchment paper or silpat mats. On a lightly floured work surface, roll out one rectangle of dough to a scant ¼-inch thickness. Using cookie cutters, cut out shapes. Using a small offset spatula, transfer the shapes to the prepared baking sheets, placing about 2 inches apart. Chill in the freezer or refrigerator until firm, about 15 minutes. Set the scraps aside. Repeat the process with the remaining rectangle of dough. Gather all the scraps, and roll out again. Chill 15 minutes; cut out more shapes, and place on sheets.
Bake, rotating sheets halfway through, until the cookies are golden around the edges and slightly firm to the touch, about 15 minutes. Transfer the cookies to a wire rack to cool completely.
PREPARE THE ROYAL ICING:
In a large bowl, use an electric mixer to combine the sugar, meringue powder, and a scant 1/2 cup water on low speed. Beat until the mixture is fluffy yet dense, 7 to 8 minutes.
To thin the icing for flooding (filling in areas with a thin layer of icing), stir in additional water, 1 teaspoon at a time. Test the consistency by lifting a spoonful of icing and letting it drip back into the bowl; a ribbon should remain on the surface for 5 to 7 seconds.
To tint the icing, dip a toothpick or wooden skewer into food coloring, and gradually mix it in until the desired shade is reached. Use a piping bag with a fine tip to pipe the royal icing around the outside edge of each sugar cookie. Then you can use a small spoon to spoon the icing onto the cookies and spread it to the edges. Let the royal icing dry completely before storing- it may take a few hours to harden completely.
*If you don't wish to use royal icing, you can decorate the cookies with sanding sugar or sprinkles, if using, before baking.
*Cookies can be kept in an airtight container, layered between sheets of waxed or parchment paper, at room temperature for up to 3 days.