Place 1 stick unsalted butter and 4 ounces cream cheese in the bowl of a stand mixer (or large bowl if using an electric hand mixer). Place 1 large egg and 1 stick unsalted butter (for the frosting) on the counter. Let everything sit at room temperature until the butter and cream cheese are softened.
Meanwhile, place 2 1/4 cups all-purpose flour, 3 tablespoons cornstarch, 1 teaspoon baking powder, and 3/4 teaspoon kosher salt into a medium bowl and whisk to combine.
Beat the butter and cream cheese with the paddle attachment on medium speed until combined, 1 to 2 minutes. Add 1 cup granulated sugar and beat on medium speed until combined and creamy, about 1 minute, stopping and scraping the sides of the bowl down with a flexible spatula as needed.
Add the egg, 2 teaspoons vanilla extract, and 1/4 teaspoon almond extract. Beat on medium speed until incorporated and lightened in color, about 30 seconds. Add the flour mixture and beat on the lowest speed until just combined. Transfer the dough to a sheet of plastic wrap and shape into a disc. Wrap the dough up in the plastic wrap. Refrigerate for at least 1 hour or up to 3 days.
Arrange 2 racks to divide the oven into thirds and heat the oven to 350°F. Line 2 baking sheets with parchment paper or silicone baking mats.
Lightly flour a work surface. Unwrap the dough and place on the flour. Lightly flour the top of the dough and a rolling pin. Roll out the dough until 1/2-inch thick. Cut cookies out with a floured 3-inch cookie cutter (or use a round cutter 3-inches in diameter), dipping the cutter in flour as needed between cuts.
Gather the scraps and form them into a ball. Roll out again until 1/2-inch thick and cut out more cookies. Only re-roll the dough once and discard any remaining dough. Transfer the rounds onto the baking sheets, 9 per baking sheet, spacing them evenly apart.
Bake for 6 minutes. Rotate the baking sheets between racks and from front to back. Bake until the edges of the cookies are set and light golden brown, 4 to 7 minutes more. The cookies may appear a bit underdone in the center but they will finish cooking as they cool. Let the cookies cool completely on the baking sheets, about 1 hour. Meanwhile, make the frosting.
Wash and dry the mixing bowl. Place the remaining 1 stick softened unsalted butter and 1/8 teaspoon kosher in the bowl. Beat with the whisk attachment on medium-high speed until light and fluffy, about 2 minutes.
With the mixer on low speed, slowly beat in 2 cups powdered sugar in 3 to 4 increments. Continue beating on medium speed until light and fluffy again, 1 to 2 minutes. Add 1 tablespoon milk and 1 teaspoon vanilla extract, and beat until combined. For colored frosting, add a few drops of food coloring if desired and beat until combined.
Spread a thick layer of frosting over each cookie with an offset spatula or butter knife. Decorate with sprinkles if desired.
