Cream butter in a medium mixing bowl; gradually add 1 cup sugar, beating well. Add 1 egg and vanilla; beat well.
Sift together flour and baking powder. Gradually add to creamed mixture; stir well. Cover and chill 1 hour.
Divide dough in half, keeping one half chilled. Roll to 1/8-inch thickness on a well-floured surface, and cut with a 2 1/2-inch round cutter.
Place on greased cookie sheets; brush with egg white. Combine remaining sugar and cinnamon in a small mixing bowl; sprinkle half of sugar mixture over cookies.
Bake at 350° for 10 minutes or until lightly browned. Cool slightly on cookie sheets, and remove to wire racks. Repeat procedure with remaining dough, egg whites, and sugar mixture.