Preheat your oven to 200c/400f and line a mini muffin/petit fours tin with mini muffin cases. The recipe makes 28-30 cakes. So if you only have a 24-hole cake tin, you can spoon the remainder of the mixture into a large muffin case (this is your cooks treat - just cook for 7-10 mins longer) or cook the rest in a second batch.
Add the sugar and egg to a large bowl and mix using a fork or balloon whisk. Add in the oil and vanilla extract, stir, and then add in the yogurt and stir to combine. Next add in the flour and baking soda, cinnamon, ginger and mixed spice and mix together using a wooden spoon. Gently fold in the chopped blackberries that have already been mixed with the 1/2tbsp of flour.
Take your mini muffin tin and fill each cake case with a heaped teaspoon of the cake mixture - so it comes almost to the top of the case. Try to evenly distribute the berries. If any of your cakes are mostly berry with just a little cake mixture, they'll collapse. Place in the oven and cook at 200c/400f for 9-10 minutes. Once cooked, leave to cool in the tin for 10 minutes before removing and cooling further on a cooling rack.
Whilst the mini muffins are in the oven, make your frosting. Take 15 blackberries, chop them in half and put to one side (for the topping). Chop the rest of your blackberries into quarters and place in a bowl with the caster sugar and ginger. Give a gentle mix and then leave to macerate for 10 minutes. Once the juices have been released, push this juicy mixture through a sieve and add approx. one quarter of the powdered sugar to the liquid. Whisk together until all lumps have disappeared. You're looking for a thick paste, so you may need to add a little more powdered sugar
In a separate bowl, whisk together the rest of the powdered sugar with the vanilla extract and 1 tbsp of cream. Continue to add the cream whilst whisking until you have a thick frosting that will hold it's shape when piped. Add the blackberry paste to the vanilla frosting and give it a little swirl with a fork. Don't over-mix - or you'll just end up with plain pink frosting. Spoon the frosting into a piping bag with a wide round nozzle and pipe onto the cooled mini muffins.