Preheat the oven to 155°C (310°F) / fan 135°C (275°F) / gas mark 3.
Spread the oats on a baking tray and toast in the oven for 15–20 minutes, stirring occasionally, until golden.
Set aside to cool completely.
In a large mixing bowl, whisk the eggs, oil, and muscovado sugar until well combined. You can also use a stand mixer fitted with the beater attachment.
Add the buckwheat flour, cooled toasted oats, baking powder, and salt to the wet .
Mix until just combined.
Gently fold in the grated pear until it is evenly distributed throughout the batter.
Divide the batter evenly between 16 cupcake moulds.
Bake for 20–25 minutes, or until a skewer inserted into the centre comes out clean.
Let the cupcakes cool in their moulds for 10 minutes before transferring them to a wire rack to cool completely.
To make the icing, gently melt the white chocolate. You can do this in a heatproof bowl set over a pan of simmering water (don't let the bowl touch the water) or in the microwave on a low power setting, stirring frequently.
In a separate bowl, beat the softened butter until creamy.
Add the sifted icing sugar and beat again until smooth.
Fold in the melted and slightly cooled white chocolate until thoroughly combined.
Once the cupcakes are completely cool, pipe the icing on top using a piping bag with a fluted nozzle, or simply spread it on with a spatula.
Garnish with white chocolate shavings made with a vegetable peeler.
