Preheat oven to 350F. Line a 12-cup muffin pan with paper cups or spray with oil (Usually i end up using mini muffin tins to make these for the kids instead of just 12 big ones). Stir flour with cocoa, baking powder, baking soda and salt in a large bowl. Purée beets in a blender or food processor. Beat sugar with oil in a medium-sized bowl, using an electric mixer, until combined, 2 min. Beat in egg, then beets and vanilla. Gradually beat in one-third of flour mixture just until blended, then half of buttermilk. Repeat additions, ending with flour mixture. Divide batter among muffin cups, filling each 3/4 full. Bake in centre of oven until a cake tester inserted in cupcakes comes out clean, 20 to 25 min. Cool in pan on a rack for 15 min, then remove cakes to a rack to cool completely. Normally I just leave these plain for the kids but you could put icing on if you feel like it.
If you dont have buttermilk, this is the substitution i always use. Take just under a cup of milk and mix 1 tablespoon of white vinegar or lemon juice into it and wait for 5 minutes and then just use like buttermilk. Works great!