Pre heat oven to 150 C / Fan 130 C / Gas 2. Grease a 20x30cm or similar-sized tin.
Mix all the dry ingredients together. Make a well in the centre, then pour in the melted butter and vanilla. Stir, then gradually add the beaten eggs, mixing till smooth. Finally, gently stir in the peanut butter. Tip into the prepared tin, and smooth out.
Bake in the middle of the preheated oven for 50 to 60 minutes. Leave to cool to room temperature before slicing.