In a medium bowl, use an electric mixer to combine the butter and sugar.
Then mix in egg yolks and almond extract, beating until blended.
Add the flour, salt and almonds to the bowl, and mix just until combined.
Cover the bowl with plastic wrap and refrigerate for one hour.
Preheat the oven to 350 degrees F. Line baking sheets with silpat mats or parchment paper.
Shape the dough into 1-inch balls.
In a small bowl, lightly beat the eggs whites with a fork.
Dip the top of each ball in egg white, then place egg-white-side-up on the cookie sheet.
Sprinkle a few slivered almonds on top and press the ball down slightly with your hand or with the bottom of a drinking glass.
Bake 13 to 15 minutes, or until the cookies spread out a bit and turn golden on the edges.
Remove from the oven and sprinkle lightly with powdered sugar.
Store these cookies in a covered container for up to 3 days, or freeze in a covered container for up to 3 weeks!