1/2 cup sugar1 cup all-purpose flour1/4 teaspoon baking powder1/4 teaspoon salt1/2 cup butter, softened1 egg1 teaspoon vanilla extract1/4 cup finely ground almondsPreheat oven to 350°F. Line a baking sheet with parchment paper.In a medium bowl, whisk together sugar, flour, baking powder, and salt. Add butter and, using an electric mixer on medium speed, beat until mixture resembles coarse crumbs. Add egg and vanilla and beat until dough comes together.Shape dough into 1-inch balls and place on prepared baking sheet. Using the bottom of a glass, press each ball into a 1 1/2-inch disk. Sprinkle with almonds. Bake until cookies are golden brown, about 12 minutes.
Stir together flour and salt. In a large mixer bowl, beat butter or margarine with electric mixer on medium speed for 30 seconds. Add sugar and beat until fluffy. Add egg yolks and vanilla; beat well. Add dry ingredients to beaten mixture and beat until well combined. Cover and chill 1 hour. For almond paste filling: In a small mixer bowl, beat egg whites and cream of tartar until soft peaks form(tips curl). Gradually add powdered sugar, beating until stiff peaks form(tips stand straight). Fold in ground almonds. Set aside. On a lightly floured surface, roll the dough to 1/8" thickness. Cut into 3" circles. Place about 1 rounded teaspoon of the almond filling in center of each. Fold up and pinch 3 sides to form a 3 cornered hat, leaving the top of filling exposed. Place 2" apart on an ungreased cookie sheet. Bake in a 375 degree oven for 10 to 12 minutes. Remove; cool on wire rack.