Mix the cocoa with the hot water and dark chocolate. Leave to cool.
Combine the flour, baking powder, salt, sugar, and baking soda in a large bowl. Whisk together.
In a separate bowl, mix the oil with the eggs, yogurt, vanilla, and crushed blackberries. Add the chilled chocolate cream. Homogenize the mixture.
Pour the liquid ingredients over the dry ones and whisk gently until smooth. Do not overmix. Use a whisk or a spatula as an electric mixer is not necessary and not recommended.
Preheat the oven to medium heat (180° C/356° F). Prepare a 12-cup muffin pan by either lining the cups with parchment paper or butter and flour them.
Put 2-3 tablespoons of the mixture in each cup, so that they are filled almost to the top. Bake for 20-25 minutes until they pass the toothpick test. When ready, place them on a rack to cool.