Preheat oven to 200°C Line a medium muffin tray (12 sections) with paper cases. Melt butter in a small saucepan or heat-proof bowl in the microwave. Set aside to cool slightly.
Sift flour into a mixing bowl. Stir in sugar. Make a well in the centre of dry ingredients.
Using a whisk, lightly beat milk, eggs and butter in a jug. Add to dry ingredients, along with mashed banana. Using a wooden spoon, gently mix ingredients until just combined. Stir in choc bits. Don't beat the mixture or the muffins will be tough.
Spoon the mixture evenly into the muffin cases. Bake for 15-20 minutes or until firm on top when lightly touched. Leave in the tray for 3 minutes. Transfer the muffins to a rack to cool.