Preheat oven to 350°F (175°C) and line a cupcake tin with liners.
Melt the dark chocolate and let it cool slightly.
In a bowl, whisk together flour, cocoa powder, baking soda, baking powder, and salt.
In another bowl, beat butter and sugar until light and fluffy. Add eggs one at a time, then mix in vanilla and melted chocolate.
Alternately add the dry ingredients and buttermilk to the batter, mixing just until combined.
Fold in chopped blackberries, then fill cupcake liners 2/3 full and bake for 18-22 minutes. Let cool completely.
For the blackberry filling, cook blackberries, sugar, lemon juice, and cornstarch in a saucepan until thickened. Let cool.
For the frosting, beat butter, powdered sugar, cocoa powder, and melted chocolate until smooth. Add heavy cream and mix until fluffy.
Cut a small hole in each cupcake, fill with blackberry filling, then pipe frosting on top. Garnish with fresh blackberries.