Make the cupcakes:

• Preheat the oven to 350°F (175°C). Line a 12-cup muffin tin with cupcake liners.
• In a medium bowl, whisk together the flour, cocoa powder, baking powder, baking soda, and salt.
• In a separate large bowl, beat together the sugar, eggs, vegetable oil, and vanilla extract until smooth and combined.
• Gradually add the dry ingredients to the wet ingredients, alternating with the milk, and mix until just combined.
• Stir in the boiling water to make the batter smooth and slightly thin.
• Gently fold in the fresh blackberries, being careful not to break them up too much.

Bake the cupcakes:

• Divide the batter evenly among the cupcake liners, filling each about 2/3 full.
• Bake in the preheated oven for 18-22 minutes, or until a toothpick inserted into the center comes out clean.
• Allow the cupcakes to cool in the tin for 5 minutes, then transfer them to a wire rack to cool completely.

Make the frosting:

• In a large bowl, beat the softened butter with an electric mixer until smooth and creamy.
• Gradually add the powdered sugar, one cup at a time, mixing well after each addition.
• Add the mashed blackberries and vanilla extract, then beat until the frosting is light and fluffy.
• If the frosting is too thick, add heavy cream, one tablespoon at a time, until you reach your desired consistency.

Frost the cupcakes:

• Once the cupcakes are completely cooled, pipe or spread the blackberry frosting onto each cupcake.
• Optionally, garnish with fresh blackberries on top for extra flavor and decoration.

Serve:

• Serve the cupcakes at room temperature, and enjoy the rich flavor of dark chocolate paired with the sweet-tart blackberries!