Place beets on a foil-lined cookie sheet and rub with oil. Fold up the foil to make a packet, and roast the beets for 1 hour to 90 minutes, until soft. Let cool.
Once cooled, remove skins and puree beets until smooth, so that you have 3/4 cup of puree. (You can do this a day in advance to save time on baking day.)
Turn oven to 350°F.
Line two 9-inch cake pans with parchment circles and spray parchment and pan sides with nonstick flour spray, or grease with butter and coat with flour.
In the bowl of a stand mixer, beat together butter, brown sugar, and granulated sugar until light and fluffy, about 3 minutes. Mix in the eggs and vanilla, then add the beets and mix until smooth.
In another bowl, stir together flour, cocoa powder, baking soda, baking powder, grated chocolate, and salt.
Stir half of the dry ingredients into the batter until just incorporated, then all of the milk, then the remaining flour. The batter will be a bit thicker than typical cake batter.
Divide batter between pans, smoothing to the edges.
Bake for 25-35 minutes, until a toothpick inserted in the center comes out clean and the cake is pulling away from the edges of the pan. (Note that the variance in time accounts for differing oven temperatures and pans.)
Let cakes cool in their pans for 10 minutes, then turn them out onto a rack to cool completely.
To make the buttercream, combine the blackberries and lemon juice in a small saucepan and warm over medium-high heat for about 5 minutes, breaking apart the blackberries as they soften. Press the berries through a fine sieve. Discard the solids
Beat together the blackberry juice and butter until light and fluffy, then add the powdered sugar and whip until the frosting comes together, scraping down the sides and the bottom as needed.
To frost, place bottom layer on a cake plate, and add 1/2 of frosting on top. Smooth to edges, then top with second cake layer, and add remaining frosting. Decorate with blackberries.
The frosting makes enough for 1 "naked" 9-inch cake. To frost the entire cake generously, double frosting ingredients. Adapted from Fine Cooking.