Peel beets and cut into cubes. Place in a pot and cover with water, 1" over the tops. Bring to a boil and cook until beets are soft. Drain, reserving ½ cup of the beet water. Combine the ½ cup water with the beets in a blender and puree until smooth. Measure out 2 cups, set side and let cool.
Preheat oven to 375˚.
In a double boiler, melt ¼ cup of butter with the semi-sweet chocolate. Let cool slightly.
In a mixer with paddle attachment, beat the softened butter and sugar together. Add the egg and vanilla, scraping down the sides. Stir the melted chocolate and beet mixture into the butter mixture. Mix until everything is thoroughly mixed.
In a separate bowl, combine pastry flour, cocoa powder, baking soda, and salt. Add to the mixer and beat until the batter is thick and most lumps are gone.
Divide batter into 18 cupcake liners. Bake for 25-28 minutes until a toothpick comes out clean when inserted. Let cool in the pan for five minutes then remove to a cooling rack to finish.
Once cupcakes are cooled, make mascarpone frosting and frost cupcakes. Store leftovers in an airtight container for 2-3 days.