Preheat oven to 400° F. Line baking sheets with parchment paper and set aside.
In a bowl, whisk together the flour, baking powder, and salt. Set aside.
In a large bowl, combine softened butter and confectioners’ sugar using a hand mixer.¹ Beat until light and fluffy, about 1 to 2 minutes. Add the egg and vanilla, and beat until thoroughly incorporated, about 30 seconds. Scrape down sides as necessary.
With mixer on low, slowly add flour mixture to the bowl. The dough is ready when most of it sticks to the paddle. When touched, it has a little give, but does not stick to fingers.
Flour the work surface and roll dough to about 1/4-inch thick, using flour for dusting as necessary. Use cookie cutters to cut cookies and place on prepared baking sheet. Gather scraps and re-roll dough when necessary.
Bake for 7 to 8 minutes, rotating halfway through. Allow cookies to cool on baking sheet for 2 minutes, then transfer to wire rack to cool completely. Prepare icing.
Place the meringue powder and water in a large mixing bowl, and whip with the whisk attachment until foamy, about 3 minutes.
Add the powdered sugar and whip on medium speed until very stiff and thick, about 3 minutes. The royal icing should hold a stiff peak. If necessary, thin with additional water, a drop at a time, to get the desired consistency.
Transfer icing to an icing bag fitted with a small round tip (I used Wilton #2). Ice the cookies and decorate with sprinkles if desired.
Store iced sugar cookies in layers between pieces of parchment paper in an airtight container for up to 5 days.Freeze sugar cookie dough in an airtight container in the freezer for up to 3 months. Defrost dough in the refrigerator before rolling and baking.