Melt one and one-halftablespoons butter in a skillet. Add the sesame seeds. Stir and cook until lightly browned. Set one-quarter cup of the mixture aside to add to the cake batter. Reserve remaining seeds to top the frosting.
Sift together the flour, salt and baking powder and set aside. Gradually blend the sugar and vanilla with the softened one-halfcup butter. Beat in the eggs. Mix the one-quarter cup toasted sesame seeds with the flour mixture and add alternately with the milk to the butter-sugar mixture. Beat the batter for thirty seconds.
Turn the batter into a lightly floured well-greased pan (9 × 9 × 2inches). Bake for thirty-five minutes, or until a cake tester inserted into the center comes out clean. Cool in the pan for ten minutes. Turn out onto a wire rack to finish cooling. When cold, spread with sesame-seed frosting. Sprinkle top with reserved toasted sesame seeds. To serve, cut into squares.