Preheat the oven to 200°C (400°F/Gas 6). Lightly grease a 12-hole standard muffin tin orline the muffin holes with paper cases. Place the pie apple in a bowl and break it up with a knife.
Sift the flour and cinnamon into another bowl and add the sugar. Make a well in the centre. Whisk together the milk, eggs and vanilla and pour into the well. Add the cooled melted butter.
Fold the mixture gently with a metal spoon until just combined. Add the apple and stir it through the mixture. Do not overmix — the mixture will still be slightly lumpy.
Fill each muffin hole with the mixture (the holes will be quite full, but don’t worry because these muffins don’t rise as much as some) and sprinkle with the walnuts. Bake for 20–25 minutes, or until golden. Leave in the tin for 5 minutes, then turn out onto a wire rack to cool.