Toast the sliced almonds in a dry pan over medium-low heat for 3 to 4 minutes, until pale gold. Let them cool.
In a large bowl, stir the butter and powdered sugar until smooth and creamy. Mix in the almond extract, vanilla and salt.
Add the all-purpose flour, almond flour and cornstarch and stir gently until a soft dough forms.
Shape the dough into a log about 2 inches (5 cm) wide and 8 inches (20 cm) long. Wrap in parchment paper.
Chill for at least 1 hour, until very firm.
Heat the oven to 325°F (160°C) and line a baking sheet with parchment. Slice the log into rounds about 1/3 inch (8 mm) thick and place 1 inch (2.5 cm) apart. Press a few toasted almond slices into the top of each cookie. Bake for 14 to 16 minutes, until the edges are pale golden.
Cool on the pan for 5 minutes, then move to a wire rack to cool completely.