Line a large baking sheet or a couple large plates (whatever your refrigerator has room for) with parchment paper. Set aside.

In a large bowl using a handheld or a stand mixer fitted with a paddle attachment, beat the butter and sugar together on high speed until completely smooth and creamy, about 3 minutes. Scrape down the sides and bottom of the bowl as needed. (Here’s a helpful tutorial if you need guidance on how to cream butter and sugar.) Add the vanilla and almond extracts and beat on medium-high speed until combined. Add the flour, cornstarch, almonds, and salt. Beat on low speed until mostly combined, then turn the mixer up to medium-high speed and beat until the dough fully comes together. The dough will be super thick, to the point where you don’t think it will combine. Just keep mixing until it clumps together. If absolutely needed, beat in a couple drops of water to get it to come together.

Scoop 1 Tablespoon (20g) of cookie dough and shape into a crescent moon. Place on the lined baking sheet/plate, and repeat with remaining cookie dough. (The shaped cookies can be close together in this step, as you’ll separate them on lined baking sheets to bake.) Refrigerate the shaped cookies for at least 30 minutes and up to 1 day. If refrigerating for longer than a couple of hours, cover the dough.

Preheat oven to 350°F (177°C). Line large baking sheets with parchment paper or silicone baking mats. Arrange the chilled cookies 2 inches apart on the prepared baking sheets.

Bake the cookies until golden brown on the bottom edges and just barely browned on top, 14–16 minutes. Allow the cookies to cool for 5 minutes on the baking sheet, then transfer them to a cooling rack to cool completely.

Gently roll each crescent cookie in the confectioners’ sugar to coat completely.

Cookies stay fresh covered at room temperature for up to 1 week.