Line a half sheet pan with parchment or Silpat. Set a rack in the center of the oven, and preheat to 325°F.
Cream the butter and brown sugar together in the bowl of a stand mixer until smooth and creamy.
Add the salt, orange zest, and vanilla and mix until well-combined.
Add the eggs and yolk, one at a time, mixing until combined and scraping the bowl as necessary.
Add the self-rising flour and mix until just combined.
Fold in the dried cranberries, white chocolate chips, and crystallized ginger until evenly distributed.
Using an offset spatula, spread the dough evenly in the prepared pan.
Bake for 10 minutes. Then rotate the pan and continue to bake until the base is golden brown and fairly firm, an additional 10 to 12 minutes.
Remove the pan from the oven and let it cool on a rack.
Frosting
Whip the cream cheese in the bowl of a stand mixer fitted with the whisk attachment until light.
Add the sugar, salt, and orange zest.
Mix on low speed until the sugar is incorporated.
Increase the mixer speed to medium-high and whip until light.
Add the lemon juice and mix to combine.
Once the bars have cooled, spread the frosting in a thin layer with an offset spatula. Don’t be too concerned with being neat at the very edges since you will be trimming them.
Topping
Sprinkle the cranberries evenly over the bars.
In a microwave-safe bowl, heat the white chocolate chips and oil together in 20-second bursts at 50% power, stirring in between, until melted.
Scrape the melted chocolate into a zip-top bag. Snip off a tiny corner and drizzle the white chocolate in a cross-hatch pattern over the berries.
Refrigerate for an hour.
Using a pizza wheel, trim the edges of the bars to make an even rectangle. Cut vertically into thirds and horizontally into fourths. You will end up with 12 squares. If you would like dessert-size bars, cut each square diagonally in half to make 24 triangles. If you would like cookie-size bars, cut each triangle diagonally in half again for a total of 48 triangles.