Sift the Dry Ingredients - In a medium bowl, sift together the flour, cornstarch, baking powder, and baking soda. Add the salt, and whisk to combine. Set aside.
Mix Butter and Sugar - In a stand mixer fitted with the paddle attachment, add the softened butter and powdered sugar. Pulse until the sugar is just incorporated. Increase speed to medium-low (setting 4), and mix until light and fluffy, 2 minutes. Scrape down the sides of the bowl with a spatula.
Add Wet Ingredients - Add the room temperature egg, vanilla extract, and almond extract. Mix on medium-high speed (setting 6) until combined, 20 to 30 seconds. Add sour cream and mix until combined, 10 seconds. Scrape down the paddle, side, and bottom of the bowl.
Add Dry Ingredients - Add the flour mixture to the mixer. Pulse on and off 8 times. Scrape down the sides of the bowl. Mix on low speed (setting 2) until the dough just comes together, 10 to 15 seconds. Do not overmix. Use a spatula to give a final mix. The dough will have a slightly tacky consistency. It will get drier once chilled.
Chill the Dough - Refrigerate in the bowl uncovered, for at least 1 hour or freeze for 45 minutes. After that time, if not baking right away, place the dough in a resealable plastic bag for up to 5 days or freeze it for up to 1 month. Defrost before using.
Preheat the Oven - Set the oven rack to the middle position. Heat to 375ºF (191ºC). Line two baking sheets with parchment paper, then set aside.
Roll Out the Dough - Generously dust the work surface, top and bottom of the dough, and rolling pin with cake flour. Use more as needed, as the dough is slightly sticky and soft. Roll to slightly thicker than 1/4".Working quickly, use a 2 ½ to 2 ¾" round cookie cutter to create circles. Dip the cutter into a bowl of flour to prevent sticking. Transfer the pieces to the parchment paper-lined sheet pans, about 1 to 2" apart. Any extra dough scraps can be rerolled out 1 more time. If needed, chill before rolling.
Bake - Working one tray at a time, bake until the surface is dry and pale in color and the bottoms are very lightly golden brown, about 8 to 9 minutes.
Cool the Cookies - Immediately transfer them to the wire rack after removing them from the oven. Completely cool before decorating, about 30 minutes. Bake the remaining cookies.
Make the Frosting - In a stand mixer fitted with the paddle attachment, mix the softened butter on medium-high speed (setting 8) until smooth, about 30 seconds. Scrape down the sides of the bowl. Add the powdered sugar, 2 tablespoons of milk, and vanilla extract. Mix on the lowest speed (stir setting) until combined, 15 seconds. Mix on medium-high speed (setting 8) until fluffy, 2 minutes. Scrape down the bowl halfway through mixing. Add 1 tablespoon of milk, and mix on medium-high speed (setting 8) until smooth and fluffy, 15 to 30 seconds.Adjust the Consistency (2 options): #1) For a thin frosting: add an additional 1 teaspoon of milk, and mix on medium-high speed for 15 seconds. Add more milk to thin. #2) For a thicker frosting: add 1 tablespoon of powdered sugar, and mix on medium-high speed (setting 8) until smooth, about 15 seconds. Add more powdered sugar to thicken.If desired, add gel coloring or food coloring and mix on slow speed (setting 2) until combined. I used 8 to 10 drops of pink gel coloring. Use immediately or cover with plastic wrap. Refrigerate if not used right away.
Notes
Frosting Yield: 1 1/2 cups
Weighing the Flour: Use a digital scale for the most accurate results. Alternatively, dip the measuring cup into the flour, then sweep off the excess flour. This makes for a denser measurement, but don’t pack the flour in the cup.
Using Only Butter: You can use all butter, but note that the cookies will not be as tall.
Make-Ahead: The dough can be mixed and stored in the refrigerator for up to 5 days, or 1 month frozen. Unbaked cut-out cookies can be covered and refrigerated for up to 5 days, or frozen for 2 weeks.
Storing Cookies: Store undecorated cookies in an airtight container at room temperature for up to 5 to 7 days, or freeze for up to 3 months. For decorated cookies, allow drying for about 1 hour, then store in an airtight container in a cool, dry place for up to 3 days, refrigerated for 1 week, or frozen for 3 months.
Storing Frosting: Store in an airtight container in the refrigerator for up to 5 days. Leave on the countertop until spreadable, just under room temperature, about 1 hour. Stir before using.