Prepare the brownies according to the package directions, replacing the oil with yogurt, and adding 1/2 tsp peppermint extract to the brownie batter. Bake brownies according to the package directions.
Meanwhile, in a small bowl, mix together the white chocolate pudding mix and 1 cup of milk. In a separate bowl, mix together the chocolate pudding mix, 1 cup of milk, and 1/4 tsp peppermint extract. Next, divide the Cool Whip between the two pudding mixtures, and fold it in until each mixture is combined.
Once brownies are completely cooled, cut into very small squares, and begin creating the layers in a large glass dish, or in small glass cups for individual trifles. Start with the brownie layer, (I like to space brownies out a bit, so you will have an equal amount for both layers). Follow with the chocolate peppermint pudding, and the white chocolate pudding layers. Repeat layers, ending with the white chocolate pudding, (or top with some additional plain Cool Whip for a pretty presentation).
Store in the fridge until read to serve. Just before serving, top with crushed candy cane or peppermint bark if desired.