Preheat oven to 350F (175C) and line a baking sheet with parchment paper. Set aside.
In a large mixing bowl, use an electric mixer (or stand mixer) to beat together butter and sugar until creamy and well-combined (about 1 minute on medium speed).
Add egg, vanilla extract, and almond extract and beat on medium-speed until completely combined. Be sure to scrape the sides and bottom of the bowl so ingredients are thoroughly combined.
In a separate mixing bowl, whisk together flour, cornstarch, baking powder, and salt.
With mixer on low-speed, very gradually add flour mixture to butter mixture until completely combined. This is a fairly dry dough, the best way to keep it from being dry and crumbly is to add the flour slowly (in 4-5 parts) and make sure it's all been incorporated before adding the next bit of flour.
Form the dough into a disk and transfer it to a clean, lightly floured surface and sprinkle the surface of the dough lightly with additional flour.
Use a lightly floured rolling pin to roll dough to be about ¼" (6.5mm) thick. As you roll, occasionally use a spatula to scrape beneath the dough to loosen it from the counter to ensure it isn't sticking to the surface. If your dough is sticky at all, simply sprinkle it with additional flour.
Use cookie cutters to cut shapes out of the dough (keep your cookie cuts close and re-group and re-roll out any dough scraps!) and transfer to prepared baking sheet, spacing cookies at least 1" apart.
Transfer to center rack of 350F (175C) oven and bake for 8-10 minutes (this is the suggested time for 2.5-3"/7.5cm cookies; smaller cookies will need less time and larger cookies may need longer). When cookies are finished baking, edges will be beginning to turn very light golden brown.
Allow cookies to cool on baking sheet for 5-10 minutes before using a cookie spatula to carefully transfer to cooling rack to cool completely.