Preheat oven to 190 degrees C. Lightly grease a 23cm square pan.
Stir sesame seeds into melted butter, and set aside to cool. Sift together the flour, baking powder and salt. In a medium bowl, mix the eggs, sugar and vanilla into the butter mixture. Add dry ingredients and stir until well blended.
Pour batter into the prepared pan, spread evenly. Bake for 20 to 25 minutes in the preheated oven. Cool and cut into squares.