Preheat the oven to 170°C / 150°C fan and line a cupcake tray with 12 cupcake cases.
Chop the blackberries into quarters and set aside.
Sieve the gluten free flour into a large mixing bowl. Add the xanthan gum, baking powder and salt and whisk everything together until well combined.
Add the butter and sugar to the bowl of an electric stand mixer and beat on a high speed until pale and fluffy - about 4 minutes.
Add one egg followed by one tbsp of the flour mixture and mix on a medium speed until combined. Repeat with the two remaining eggs.
Add the Greek yoghurt and vanilla extract and mix again.
Add the remaining flour mixture and mix on a low speed until just combined, scraping down the sides if necessary.
Distribute the batter evenly into the cupcake cases. Each case should be about 3/4 of the way full.
Push 8 pieces of the chopped blackberry into each of the cupcakes (to equal 2 whole blackberries per cupcake). As the batter is quite thick, you might need to use a small spoon or knife to make pockets in the batter that you can easily push the pieces into. Try to distribute the blackberry pieces throughout the batter, with some nearer the top and some nearer the bottom.
Bake for around 20 minutes or until a skewer poked into the centre of a cake comes out clean or with just a few moist crumbs.
Leave to cool completely before frosting.