Preheat the oven to 350 degrees F. Line a 9-inch x 13-inch baking pan with parchment paper. Set aside.
In a medium mixing bowl, whisk together the flour, baking powder, salt, and ginger. Set aside.
In a large mixing bowl, beat together the butter, oil, brown sugar, granulated sugar, and orange zest until smooth. Add the eggs and vanilla and mix well.
Add the flour mixture to the wet ingredients and stir until just combined. Gently fold in the white chocolate and dried cranberries with a rubber spatula or wooden spoon.
Transfer the mixture to the prepared pan and spread it out into an even layer.
Bake for 30 minutes, or until a toothpick inserted into the center comes out clean or with a few moist crumbs. Remove from the oven and allow to cool completely in the pan on a wire rack.
Topping
In a large mixing bowl, beat together the cream cheese and half of the melted white chocolate until well combined. Add the powdered sugar and mix until smooth. Stir in the vanilla extract.
Spread the frosting evenly over the cooled bars, then sprinkle with the chopped cranberries. Drizzle the remaining white chocolate in a zig-zag pattern over the top, and then sprinkle with orange zest.
Divide the block into 8 rectangles by cutting it in half vertically and then three more times horizontally. Then cut each rectangle diagonally to form 16 triangle bars.