Preheat oven to 180C.

Dry roast the walnuts and let cool.

Break the roasted walnuts into smaller pieces, setting some aside for topping.

Chop the apple into small, bite-sized pieces.

Heat the ingredients (unspecified) in a saucepan over medium heat.

Bring to a boil, then reduce heat to low and cook until moisture is reduced.

In a bowl, mix olive oil, maple syrup, and the cooled mixture from the saucepan.

Stir in the soy milk.

Fold in the cake flour, baking powder, and brown sugar.

Add the chopped walnuts (excluding those set aside for topping).

Pour the batter into muffin cups.

Top with the reserved walnuts, lightly pressing them into the batter.

Bake for 20 minutes, or until a skewer inserted into the center comes out clean.

Let cool slightly before serving.