Preheat oven to 325°F. Line two baking sheets with parchment.
Beat butter and confectioners' sugar until smooth and fluffy, about 2 minutes.
Mix in amaretto, vanilla, almond extract, and salt until combined.
Whisk flour and cornstarch, then add to the bowl. Blend just until a soft dough forms.
Chill dough 15 minutes to firm slightly for easier rolling.
Roll dough between parchment to 1/4-inch thickness. Cut 2-inch rounds or shapes.
Arrange on sheets 1 inch apart. Sprinkle with coarse sugar and almonds, pressing gently.
Bake 12–14 minutes, until edges look set and barely golden. Do not overbrown.
Cool 5 minutes on the sheet, then move to a rack to cool completely.