Preheat your oven to 350°F (175°C). Grease and line the bottoms of the two 9-inch round cake pans with parchment paper.
In a mixing bowl, whisk together the flour, sugar, cocoa powder, baking powder, baking soda, and salt until well combined.
Add the eggs, milk, vegetable oil, and vanilla extract to the dry ingredients. Beat with an electric mixer on medium speed for 2 minutes until the batter is smooth.
Carefully stir in the boiling water until fully incorporated. The batter will be thin.
Pour the batter evenly into the prepared cake pans and bake for 30-35 minutes, or until a toothpick inserted in the center comes out clean. Remove from the oven and let cool in the pans for 10 minutes before transferring to a cooling rack.
While the cakes are cooling, prepare the blackberry filling. In a saucepan, combine the blackberries, sugar, cornstarch, and lemon juice. Cook over medium heat until the mixture starts to bubble and thicken, about 5-7 minutes. Remove from heat and let cool.
For the frosting, beat the softened butter in a mixing bowl until creamy. Gradually add the powdered sugar and cocoa powder, mixing on low speed until combined. Add the heavy cream and vanilla extract, then increase the speed and beat until fluffy.
Once the cakes are completely cooled, place one layer on a serving plate. Spread half of the blackberry filling on top, then add the second cake layer.
Frost the top and sides of the cake with the chocolate frosting. Use the remaining blackberry filling to decorate on top or between layers, and garnish with extra blackberries if desired.
Slice and serve!