In a large bowl, cream butter and sugar until light and fluffy, about 2-3 minutes on medium speed.
1 cup butter, 1 cup granulated sugar
Beat in eggs, egg yolks and extracts.
2 large eggs, 2 large egg yolks, 2 teaspoons vanilla extract, ½ teaspoon almond extract
Add the flour, baking powder and salt, and mix in the dry ingredients in just until combined.
3 ½ cups all-purpose flour, 1 ½ teaspoons baking powder, ¼ teaspoon salt
Shape into a disk.
Wrap tightly in plastic wrap and refrigerate for at least 1 hour or until firm enough to roll.
Toward the end of the chilling time, preheat oven to 350F. Line two cookie sheets with either parchment paper or silicone baking mats.
On a lightly powdered sugared surface, roll dough to 1/2-in. thickness.
Dip a 2-inch round cookie cutter in powdered sugar, and use the dipped cookie cutter to cut out the dough.
Place the cut dough 2 inches apart on the prepared cookie sheets.
Bake until the cookies are set, about 10-12 minutes. The edges should just be beginning to turn light golden brown but shouldn't be brown.
Cool on pans 5 minutes.
Remove to wire racks to cool completely.
To make the frosting, beat the butter in a medium mixer until pale, about 1-2 minutes on medium speed.
1 cup butter
Add the powdered sugar, vanilla extract, salt, and heavy cream. Beat until well-combined. Add in additional powdered sugar to thicken the frosting or additional cream to thin the frosting to reach a spreadable consistency.
3 ½ cups sifted powdered sugar, ½ cup heavy cream, 1 teaspoon vanilla extract, ¼ teaspoon kosher salt
Mix in food coloring, if using.
Spread the frosting over the cooled cookies.
Notes
Butter: I use salted butter in this recipe. If you're using unsalted butter, increase the salt in the cookies to 3/4 teaspoon.
Almond extract: The hint of almond extract gives the cookies that classic sugar cookie flavor. If you can't use almond extract, you can substitute additional vanilla extract.
Flour: Weighing the flour is the most accurate way to measure it. I highly recommend weighing the flour. If not, sift the flour, then lightly spoon it into the measuring cup and level. Avoid packing the flour. That will give you dry, heavy cookies.
Kosher salt: If you're using table salt, use half the amount of salt.