Beat butter at medium speed of an electric mixer until creamy; gradually add 1/2 cup sugar, beating well. Add 1 egg and vanilla; beat well. Gradually add flour; beat well.
Shape dough into 48 (1") balls; press balls into lightly greased miniature (1 3/4") muffin pans, pressing evenly into bottom and up sides. Set aside.
Beat almond paste at medium speed until creamy; gradually add remaining 1/2 cup sugar, beating well.
Add almond extract and remaining 2 eggs, beating well. Spoon mixture into prepared shells. Top each tartlet with 3 slivered almonds. Bake at 325° for 25 minutes or until golden. Cool in pans on wire racks 10 minutes; remove to wire racks, and cool completely.