Mix butter and sugar in a stand mixer fitted with a paddle attachment or in a large bowl with an electric hand mixer on low speed for 30 seconds.
Increase speed to medium and beat until well combined and creamy, about 2-3 minutes.
Add the egg and vanilla and mix in until combined.
Whisk the flour, cornstarch, and salt together in a separate medium bowl.
Add the flour mixture to the wet ingredients little by little and mix in until just combined.
Roll the dough into a rectangle that is 1/4” inch thick on a lightly powdered sugar-covered work surface. Wrap tightly in plastic wrap and place the dough in the refrigerator for 30 minutes.
Toward the end of the chilling time, preheat the oven to 350 F.
Line two large cookie sheets with parchment paper or silicone baking mats. Set aside.
Unwrap the dough and place on a work surface that's lightly dusted with powdered sugar.
Cut the dough into circles using a round cookie cutter and place them on a baking sheet.
Bake for 12-15 minutes, or until the edges are just beginning to turn golden brown.
Let them cool for at least an hour. They must be completely cool before you add the icing.
Royal Icing
To make the royal icing, beat the powdered sugar, flavor extract, water, and meringue powder in a stand mixer or in a large bowl with an electric hand mixer until it’s fluffy and has stiff peaks, about 4 to 5 minutes.
Check the consistency of your icing. If it's too thick add more water a little at a time. For these cookies, the icing should be a medium consistency. It should take about 15 seconds to disappear. This should work for flooding and details and should not be runny so it doesn't run through the icing dam. Medium royal icing is slightly thinner than piping icing.
Once you have the consistency you want, place it into a piping bag or a plastic baggie. If you are using a piping bag, seal it with a knot or with a rubber band.
Cut a tiny edge of the bottom of the bag to use.
Putting it all together
Outline each cookie with the icing and continue making a spiral inwards.
Immediately use a toothpick or a similar tool to smooth the icing out.
Place the eyes on the cookie. Allow the icing to set before adding the lines.
Once the icing has set, drizzle each cookie with a bit of icing to make it look like the mummy wrapping. Be careful not to cover the eyes.
Notes
Butter: I use salted butter in these cookies. If using unsalted butter, increase the amount of salt by 1/4 teaspoon.
Vanilla extract: If you'd like the cookies to be lighter, use clear vanilla extract.
All-purpose flour: It's key to properly measure the flour. Either weigh the flour (click on "metric" for the measurements by weight) or sift/stir the flour to break it up. Lightly spoon the flour into a measuring cup and level. Avoid packing the flour as that will give you dry dough that doesn't hold together.
Clear flavor extract: It's important to use a clear flavor extract so that you don't end up with off-white cookies. Clear vanilla flavoring or almond extract work well.