Method:

Place the butter in a bowl or stand mixer and whip this and electric mixer until light and fluffy.
Gradually add the icing sugar and whip with every addition.
Once fully incorporated, add the vanilla essence and food coloring. Mix to combine. Your buttercream may be colored as desired.
Transfer the buttercream to a piping bag.
Pipe a small circle of buttercream on a plate or cake board. Place a doughnut on the buttercream and secure. Pipe another on the doughnut and layer another doughnut. Repeat the process until all the doughnuts have been used.
Spoon or pipe the jam in to the centre of the cake, to the rim.
Pipe a layer on buttercream around the cake and on top of the cake. Use a cake scrapper or spatula to even the buttercream.
Decorate the cake with the mini doughnuts and sprinkles