Cream together the butter and sugar until fluffy. Add vanilla and tahini, mix until well combined. In a separate bowl, sift together the flour and baking powder, then stir into butter mixture. Drop onto an ungreased baking tray in tablespoon-sized pieces.
Bake in preheated oven until they turn golden brown, about 15 minutes. Cool on the baking tray 10 to 15 minutes before removing to cool completely on a wire rack.