Line an air fryer–safe baking pan with parchment paper, leaving an overhang on two sides.
Beat the melted butter and brown sugar on medium speed with an electric mixer until smooth. Add the eggs, 1 teaspoon orange extract, and 1 teaspoon vanilla extract, and beat until fully combined.
Add the ground ginger, baking powder, salt, and flour. Beat just until the flour disappears. Do not overmix.
Stir in the white chocolate chips and chopped cranberries by hand. Spread the batter evenly into the bottom of the prepared pan.
Place the pan in the air fryer and cook at 320°F for 10–16 minutes, until the edges are golden and set and a toothpick comes out with a few moist crumbs. Start checking at 10 minutes.
Move the pan to a wire rack and cool the bars completely to room temperature, about 1 hour.
Beat the softened cream cheese and powdered sugar with a whisk or electric mixer until smooth and creamy. Add 1/2 teaspoon orange extract and 1/2 teaspoon vanilla extract and mix well.
Spread the frosting over the cooled bars. Sprinkle with the chopped cranberries, then drizzle the melted white chocolate over the top with a fork.
Refrigerate for 20–30 minutes to set the frosting. Cut into 16 squares, then slice each square diagonally into triangles.