Preheat oven to 180 C / Gas 4. Line a muffin tin with paper cases.
Whisk flour, baking powder and salt together in a bowl.
Combine brown sugar, peanut butter and butter in another bowl; beat together with an electric mixer until creamy. Beat in egg and vanilla extract. Mix in flour mixture and milk; beat until smooth. Fold chocolate chips into the mixture.
Spoon the cupcake batter into the prepared muffin tin.
Bake in the preheated oven until a skewer inserted into the centre comes out clean, 20 to 25 minutes. Transfer to a wire rack to cool, about 30 minutes.