To make the dough: In a large mixing bowl, the bowl of a stand mixer, or a food processor, combine the flour, confectioners’ sugar, salt, baking powder, and baking soda. Stir or pulse until evenly incorporated.

Add the butter cubes and work them into the dry ingredients until fine, even crumbs form; this can be done by breaking up the butter with your fingers or a fork, mixing on low speed with the flat beater of a stand mixer, or pulsing in a food processor.

Separate the egg, placing the white in a small measuring cup. Set aside. Add the egg yolk to the butter-coated dry ingredients, stirring or pulsing until evenly blended.

Lightly whisk the milk into the egg white, then measure out 1 tablespoon of this mixture by pouring from the measuring cup into the measuring spoon (rather than scooping) or by weighing out 14g. Add it to the bowl.

Add the vanilla and mix or pulse the ingredients briefly until larger clumps start to form. Use your hands to bring the dough together into one mass.

Transfer the dough to a piece of parchment or wax paper, cover with a second piece, and roll the dough out until it’s about ½" thick.

Refrigerate the dough, still covered with paper, for about 30 minutes.

Preheat the oven to 325°F. Line a baking sheet with parchment.

Remove the dough from the refrigerator and continue to roll it, still sandwiched between parchment or wax paper, until it’s ¼"-thick. Use a light dusting of flour, if necessary, to prevent the dough from sticking to the paper or your rolling pin.

Cut out your desired cookie shapes and transfer them to the prepared baking sheet.

Bake the sugar cookies for 14 to 18 minutes, until their bottoms just start to turn golden; you'll see little to no color on the tops and sides of the cookies.

Remove the sugar cookies from the oven and immediately transfer them, still on the parchment, to a rack to cool completely.

To make the frosting: In a medium bowl, stir together all the ingredients in the order listed, adding enough milk to make the glaze spreadable and smooth; it shouldn’t be runny. Color as desired.

Spread the frosting onto the cooled cookies with an offset spatula or dull knife. Top the freshly frosted cookies with sprinkles or decorating sugars, then set the cookies aside until the glaze is set, about 30 minutes.