Preheat oven to 180 C / Gas 4. Line a muffin tin with paper cases.
Whisk flour, bicarbonate of soda, baking powder and salt together in a bowl.
Combine caster sugar, brown sugar and 55g butter in another bowl; beat with an electric mixer until creamy. Beat in egg. Mix in mashed bananas. Add flour mixture in 3 batches, alternating with buttermilk, stirring after each addition. Fold chocolate chips into the cupcake batter.
Spoon mixture evenly into the prepared muffin cases.
Bake in the preheated oven until a skewer inserted in the centre comes out clean, about 20 minutes. Cool cupcakes on a wire rack, about 30 minutes.
Beat cream cheese and 3 tablespoons butter in a bowl until smooth. Add vanilla extract. Beat in icing sugar, about 125g at a time, until frosting is smooth.