Preheat the oven to 350 F. Line 2 cupcakes pans with 24 cupcake papers. In a stand mixer, cream the butter and sugar on high for 2-3 minutes or until light colored and fluffy. Beat in the eggs one at a time. Beat in the vanilla.
In a separate bowl, whisk together the flour and baking powder. Alternately add the dry ingredients to the wet ingredients with the milk in three parts, stirring just until combined and scraping down the sides as necessary.
Spoon the batter into the lined cupcakes pan, dividing between all 24. Bake for 20-15 minutes or until a toothpick inserted comes out clean. Let cool for 5 minutes in the pan and then remove to a wire rack to cool completely.
To make the buttercream, place the blackberries, lemon juice and water in a small saucepan. Heat on medium heat stirring occasionally until the blackberries soften and release their juice. Crush the blackberries and continue to cook the mixture on the stove to reduce it. When the mixture coats the back of the spoon, remove from the heat and strain the mixture in a fine mesh strainer to remove the seeds and fruit. You should have roughly 1/4 cup of liquid. Let cool completely
Beat the softened butter in a stand mixer for 2-3 minutes until light in color and fluffy. Beat in the powdered sugar, vanilla, blackberry reduction and enough of the heavy cream or milk to make a spreadable consistency. Beat the frosting on high for 3-4 minutes or until very fluffy. Pipe the frosting onto cooled cupcakes and garnish with a blackberry if desired.