Combine the butter and the sugar in the bowl of an electric mixer and mix until fluffy, about 3 minutes. Add the eggs and cointreau and mix until incorporated. Add the pureed orange mixture and mix until incorporated. In a separate bowl, combine the dry ingredients. Add the dry ingredients to the batter and mix until well incorporated.
Pour into prepared pan and bake until the center springs back, about 25 to 30 minutes. Remove from the oven and cool. Cut the cake into 24 equal pieces. To assemble, place one piece of the cake in the center of 12 plates. Place 1/4 cup of the ice cream on top of each piece of the cake. Spoon some of the compote over the ice cream. Place another piece of cake on top of the compote, forming a sandwich. Repeat the above process with the remaining ice cream and compote. Garnish with mint sprigs and a sprinkle of confectioners' sugar.