To prepare crust: Position rack in center of oven; preheat to 350°F. Coat an 8-inch-square baking pan with cooking spray.
Beat butter, 2 tablespoons granulated sugar and brown sugar in a medium bowl with an electric mixer until creamy. Stir in whole-wheat flour, 1/3 cup all-purpose flour and salt until well combined (the mixture will still be crumbly). Evenly press the mixture into the bottom of the prepared pan. Bake until just barely golden around the edges, 10 to 12 minutes.
To prepare topping: Combine 3/4 cup granulated sugar, 2 tablespoons all-purpose flour, baking powder and salt in a medium bowl. Add egg, egg white, orange zest and juice; stir until blended and smooth.
Sprinkle cranberries over the baked crust. Pour the orange mixture over the cranberries and sprinkle with pistachios.
Bake until golden and set, 40 to 45 minutes. Let cool completely on a wire rack; if possible, chill before cutting into squares.