Grease three baking trays and line with baking paper.
Cream the butter and sugars until the mixture is pale and fluffy.
Add the egg and vanilla extract and beat again until combined.
Add the peanut butter and beat again until combined.
Fold sifted flour into the mixture until combined.
Roll mixture into balls (about 25 grams each) and place onto baking trays, leaving room for biscuits to spread.
Gently press a fork across each biscuit to flatten the biscuit and leave an indentation - and then a second time at right angles to the first indentation (creating a cross pattern).
Bake for 12-15 minutes or until a golden colour.
Allow to cool on tray for 5 minutes before transferring biscuits to a wire cooling rack to cool completely.