Place 16 mini silicone muffin cases on a baking sheet.
Sift the flour and cocoa powder into a bowl. Stir in the sugar. Put the beetroot, oil and egg in a food processor or blender and blend to make a smooth purée. Briefly blend in the buttermilk and vinegar. Add to the dry ingredients. Using a large metal spoon, stir the ingredients together until combined. Divide among the cases.
Bake in a preheated oven, 180°C (350°F), Gas Mark 4, for 10 minutes, or until risen and just firm. Leave in the cases for 2 minutes, then transfer to a wire rack to cool completely.
Make the frosting by beating together the cream cheese, butter, vanilla bean paste and icing sugar until smooth and creamy. Place in a piping bag with a small star nozzle and pipe swirls on top of each cake. Decorate each with a rose petal.