Cream butter in a medium mixing bowl; gradually add sugar, beating well. Add eggs, one at a time, beating well after each addition.
Combine flour and baking powder in a small mixing bowl; add to creamed mixture, beating well. Stir in sesame seeds and vanilla.
Drop dough by teaspoonfuls 2 inches apart onto waxed paper-lined cookie sheets. Bake at 325° for 12 to 15 minutes. Cool completely on cookie sheets. Remove from waxed paper, and store cookies in airtight containers.