Preheat the oven to 180C (350F).

Roast the walnuts for about 5 minutes.

Melt the butter in a heatproof bowl using residual oven heat.

Mash the bananas with a masher until smooth.

Sift together the cake flour and baking powder.

In a separate bowl, beat the butter until creamy.

Gradually add the granulated sugar in two batches, beating until light and fluffy.

Add the beaten egg little by little, combining well after each addition.

Incorporate the mashed bananas into the butter-sugar mixture.

Fold in the roasted walnuts.

Gently fold in half of the sifted dry ingredients until just combined.

Repeat with the remaining dry ingredients, being careful not to overmix.

Pour the batter into muffin cups, filling each about 2/3 full.

Bake for 35 minutes, or until a toothpick inserted into the center comes out clean.

Optionally, add chocolate pieces to the top of the muffins before baking.