Combine flour, salt (if butter is unsalted), baking powder, and sugar in a large bowl or the work bowl of your machine, whisking to combine well. Cut butter into small cubes and add to dry ingredients. Run the machine, scraping down as needed, until the butter fully disappears into the flour mixture, which will look sandy and clump easily between your fingertips. Add the egg and vanilla and run the machine until it blends into an even cookie dough, scraping down a few times to make sure it mixes evenly.

Combine sugar and salt (if butter is unsalted) in a large bowl or the bowl of your mixer. Cut butter into small cubes and add to the sugar mixture and beat with the paddle or beater attachments until the butter and sugar are an even, soft texture — you’ll want to scrape down the bowl a few times and be patient, especially with a hand mixer. Add egg and vanilla and beat until evenly combined, scraping down bowl. Add baking powder and beat it an additional 30 seconds beyond what is needed to make the baking powder disappear. Add flour and mix only until it disappears.

Divide dough in half and if it’s in loose chunks, gently knead it together into one mass on a sheet of parchment paper. Place a second sheet of parchment paper over the dough and roll each dough half between 2 large pieces of parchment paper into your desired thickness. Slide each parchment-and-cookie-dough slab onto the back of a baking sheet, thin tray, or thin cutting board and place in freezer for 15 to 20 minutes, until solid.

Heat oven to 350 degrees F.

Carefully remove top sheet of parchment paper from first cookie dough slab and place the side that touched the dough down on a large baking sheet. Cut cookies into your desired shape. Peel each cookie off the bottom sheet of parchment and arrange on baking sheet with 2 inches between them. Repeat with remaining slab of cookie dough. If you have any dough to reroll, do it again between two sheets of parchment paper and freeze this slab until solid again before cutting into it.

Bake cookies until they are a light golden brown at the edges, rotating trays once while baking to ensure even baking, about 10 to 12 minutes. Use cookie color as your guide, not the timer. Let cookies set for one minute on the tray after removing from the oven then transfer to a cooling rack to let the cookies cool completely. You can stop right here or you can decorate them.

Whisk your egg white (or substitute reconstituted from egg white or meringue powder) in a large bowl until loose and frothy. Add salt and 1 cup of powdered sugar, beating until smooth. Add flavorings, if desired, and last 1/4 cup of sugar. To dip your cookies, scrape half of icing into wide bowl. Add water, 1/4 teaspoon at a time to thin the frosting until it can thinly but mostly opaquely coat a dipped cookie. Scrape the remaining, thicker half of your icing into a sandwich or freezer bag, cut the tiniest nip off the corner of the bag, and pipe designs of your choice on top. If you’re adding sprinkles, do so every 3 to 4 cookies or the icing will begin set and the sprinkles won’t adhere. Let them set until completely solid.