Preheat oven to 350°F (175°C). Spray an 8x8-inch pan with cooking spray and line it with parchment paper, leaving an overhang for easy removal.
Melt butter in a light-colored, wide saucepan over medium-high heat. Once melted, reduce to medium and stir constantly with a silicone spatula. Butter will bubble and foam. When it smells nutty and you see light-brown specks under the foam, quickly remove from heat and pour butter into a bowl, scraping all the bits from the pan. Let it cool for 5 minutes.
Add the brown sugar to the cooled butter and whisk vigorously until the mixture resembles wet sand. Add the egg, vanilla, orange extract, orange zest, ginger, and salt, and whisk briskly until the mixture is very creamy and emulsified. Add the flour, white chocolate chips, and cranberries, then switch to a spatula to fold the dough until no dry streaks of flour remain. The batter will be thick.
Spread the batter evenly into the prepared pan and smooth the top with a spatula. Bake for 25–27 minutes, or until the edges are lightly golden and the top is set.
Remove from the oven and let the bars cool in the pan for 10–15 minutes. Use the parchment overhang to lift them out and transfer to a wire rack, then slide the parchment out from underneath. Let cool completely.
Frosting: Microwave softened cream cheese in 10-second bursts (waiting 30 seconds between each) until easily stirred. In a large bowl, beat cream cheese, powdered sugar, orange extract, and vanilla until smooth and creamy, scraping sides as needed. Frost completely cooled bars and top with chopped cranberries.
Add white chocolate chips and coconut oil to a small microwave-safe bowl. Microwave in 15-second bursts, stirring between each, until melted and smooth. Transfer to a zip-top bag, snip the corner, and drizzle over the bars.
Let the drizzle set. Cut into 9 squares, then slice each diagonally to create 18 triangle-shaped bars.