Mix the peanut butter with the soft butter. Stir in the brown and white sugar, add the eggs and vanilla and stir everything until creamy. Mix flour with baking powder and salt and add to the butter mixture, briefly stir in by hand (not with the mixer!), Until the dry ingredients just start to get moist.
Place in a greased form measuring 22 x 22 cm and bake in a preheated oven at 175 degrees for 30-35 minutes.