Make the cookies: Whisk the flour, baking soda and salt in a medium bowl. Beat the butter and granulated sugar in a stand mixer fitted with the paddle attachment on medium speed until fluffy. Beat in the egg, then beat in the vanilla and almond extracts. Reduce the mixer speed to low; add the flour mixture and beat until combined. Cover and chill 1 hour.
Preheat the oven to 350 degrees F. Line 2 baking sheets with parchment paper. Scoop 1-inch mounds of dough onto the prepared baking sheets, about 2 1/2 inches apart; flatten the mounds with your fingers. Bake until the cookies are golden around the edges, about 10 minutes. Let the cookies cool 10 minutes on the baking sheets, then transfer to racks to cool completely.
Make the frosting: Beat the butter, almond and vanilla extracts, and salt in a stand mixer fitted with the paddle attachment on medium speed until light and fluffy. Add the confectioners' sugar and beat until smooth and creamy. Transfer to a piping bag fitted with a small star tip. Pipe the frosting onto the cooled cookies and top with nonpareils or Jordan almonds.