Grease a large baking sheet.
Put the flour, bicarbonate of soda and sugars in a bowl. Beat the egg with the vegetable oil and milk and add to the dry ingredients.
Beat together to form a thick paste, adding a little more milk if the mixture feels crumbly.
Take teaspoonfuls of the mixture and roll into balls, about the size of a cherry, using floured hands. Space well apart on the baking sheet and flatten slightly.
Bake in a preheated oven 200°C (400°F), Gas Mark 6, for 12 minutes until the mixture has spread and is pale golden. Transfer to a wire rack to cool.
Make the filling by beating together the peanut butter, butter and icing sugar until smooth. Add the measurement hot water and beat until light and fluffy. Use to sandwich the cakes together.