Preheat oven to 180 C / 350 F. Line a 12-hole muffin tin with cupcake liners.Sift flour, sugar, cocoa powder and baking powder into a large bowl. Set aside.
Place grated beetroots, buttermilk, white vinegar and vanilla extract in a food processor. Process until smooth. Add butter and eggs. Process until just combined.Add beetroot mixture into the flour mixture. Fold in gently.
Fill each hole in the muffin tin with ¼ cup batter. Bake for 20-25 minutes or until a skewer inserted into the middle of the cupcakes come out clean. Transfer onto a wire rack to cool completely.
Cream cheese frosting:
Place butter, half of sugar and vanilla extract in a large bowl. Using an electric mixer, beat until smooth. Add remaining sugar and cream cheese. Beat until just combined.
Transfer frosting to a piping bag fitted with a star tip. Pipe frosting onto the cupcakes.