Preheat the oven to 180°C/gas mark 4. Line 2 baking trays with baking parchment.
With an electric mixer, cream together the butter, light brown sugar, caster sugar and vanilla extract.
Stir in the egg, plain flour, baking powder and peanut butter until everything is combined. Fold in the chopped nuts.
Use a teaspoon to drop walnut-sized balls on to the baking trays, allowing room for them to spread. Press down lightly with the back of the spoon and bake for 15 minutes.