In the bowl of a stand mixer with a paddle attachment (or use a hand mixer in a large bowl), cream together the butter and sugar. Add the aquafaba, almond extract, and vanilla extract, mixing to combine.

In a separate bowl, whisk together the flour, crushed candy canes, and salt. Add the dry ingredients to the wet ingredients and continue mixing just until a dough is formed.

Cover with plastic wrap and refrigerate for at least 2 hours, up to overnight, to chill thoroughly.

Preheat the oven to 375°F. Line a baking sheet with parchment paper.

Roll the chilled cookie dough into 1-inch balls. Place onto the prepared baking sheet at least 2 inches apart.

Bake for 9 minutes. (The cookies will spread slightly but will not brown.) Let the baked cookies rest for 5 minutes on the baking tray, then use a spatula to transfer to a wire rack to cool completely. Serve at room temperature.