Preheat your oven to 180°C (350°F) and line a muffin tin with cupcake liners.
In a medium bowl, combine the cocoa powder and hot water. Whisk until smooth, then add the chopped dark chocolate. Stir until melted.
In another bowl, whisk together the flour, baking powder, baking soda, and salt.
In a large bowl, beat the eggs and sugar until light and fluffy. Add oil, yogurt, and vanilla extract, mixing until combined.
Gradually add the dry ingredients to the wet mixture, alternating with the chocolate mixture. Mix until combined.
Gently fold in the crushed blackberries into the batter.
Divide the batter evenly among the muffin tin and bake for 18-20 minutes. Let cool for 5 minutes before transferring to a rack.
In a saucepan, combine 200g blackberries, 50ml water, and 2 tbsp sugar. Heat until the blackberries break down and the sauce thickens.
In a saucepan, heat the whipping cream until simmering. Pour over 200g dark chocolate, let sit, then stir until smooth. Add powdered sugar and vanilla.
Once cupcakes are cool, dip tops into ganache or spoon it over. Drizzle with blackberry sauce and garnish with fresh blackberries.