In a medium bowl, sift together the flour, cornstarch, baking powder, and baking soda. Add the salt, whisk to combine. Set aside.
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), mix until light and fluffy, 2 minutes. Scrape down the sides of the bowl with a spatula.
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 on until combined, 10 seconds. Scrape down the paddle, side, and bottom of the bowl.
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.
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 frozen for up to 1 month. Defrost before using.
Line two baking sheets with parchment paper, then set aside. Set the oven rack to the middle position. Heat to 375ºF (191ºC).
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-inch.
Working quickly, use a 2 ½ to 2 ¾-inch 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-inches apart. Any extra dough scraps can be rerolled out 1 more time. If needed, chill before rolling.
Working one tray at a time, bake until the surface is dry and pale in color, and bottoms are very lightly golden brown, about 8 to 9 minutes.
Immediately transfer to the wire rack after removing from the oven. Completely cool the cookies before decorating, about 30 minutes. Bake the remaining cookies.
Frosting (1 ½ cups)
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, mix on medium-high speed (setting 8) until smooth and fluffy, 15 to 30 seconds.For a thinner frosting: add an additional 1 teaspoon of milk, mix on medium-high speed for 15 seconds. Add more milk until the desired consistency is reached.For a thicker frosting: add in 1 tablespoon of powdered sugar, mix on medium-high speed (setting 8) until smooth, about 15 seconds. Add more powdered sugar until the desired consistency is reached.
Use the frosting as is, or add gel coloring or food coloring and mix on slow speed (setting 2) until combined. I use 8 to 10 drops of pink gel coloring. Use immediately or cover with plastic wrap. Refrigerate if not used right away.
Properly weigh 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.