Cream butter in a medium mixing bowl; add sugar and almond extract, beating until light and fluffy. Gradually add flour, beating well.
Beat egg white (at room temperature) in a small mixing bowl until stiff peaks form; gently fold into creamed mixture.
Drop dough by heaping 1/2 teaspoonfuls 1 1/2 inches apart onto greased cookie sheets. Place an almond slice on top of each, and bake at 375° for 8 minutes or until edges are golden brown. Allow cookies to stand 1 minute on cookie sheets before transferring to wire racks to cool completely. Store cookies in airtight containers.