In the bowl of a stand mixer fitted with the paddle attachment, beat the butter and sugar together at medium speed until light and fluffy, about 3 minutes.
1 cup unsalted butter, ⅔ cup granulated sugar
Add the egg, vanilla, and almond extract and beat at medium speed until well incorporated, about 1 minute.
1 large egg, 1 teaspoon pure vanilla extract, ¼ teaspoon almond extract
In a separate bowl, whisk the flour, kosher salt, and coarse sea salt together.
2¼ cups all-purpose flour, ½ teaspoon kosher salt, ¼ teaspoon coarse sea salt
In one addition, add the dry ingredients to the wet ingredients and mix on low speed just until no flour is visible. Do not overbeat the dough or the cookies will be tough.
Scrape around the sides and bottom of the bowl with a rubber spatula to ensure all of the flour has been incorporated.
Divide the dough in half and place one half on a large piece of parchment paper. Roll out the dough to be ¼-inch thick, and transfer the dough with the parchment paper to a large sheet pan.
Roll out the other half of the dough and place the rolled dough (with the parchment paper) on top of the first half of rolled dough on the sheet pan.
Cover the dough with plastic wrap and refrigerate for at least 2 hours. (To freeze the cookie dough at this point, cover the rolled dough on the baking sheet with plastic wrap and foil. Freeze until ready to bake).
After the cookie dough has chilled, preheat the oven to 350°F. Line a baking sheet with parchment paper.
Cut the rolled and chilled cookie dough into desired shapes. Place onto the prepared baking sheet.
Bake for 10-12 minutes, or until the edges and bottoms are just beginning to darken.
Remove cookies from the oven and let cool for 1 minute on the baking sheet, then use a metal spatula to transfer cookies to a cooling rack. Repeat with remaining cookies. Allow cookies to fully cool before icing.