Adjust oven rack to middle position and preheat oven to 350ºF (175ºC). Line a 9- by 13- inch rimmed baking sheet with parchment paper; set aside.
In a large bowl, whisk together all-purpose flour, white whole wheat flour, cornstarch, caster sugar, and salt until combined.
In a small saucepan, heat butter over medium-low heat until melted. (Alternatively, melt butter in a medium bowl or measuring cup in the microwave.) Pour melted butter into the flour mixture and, using a rubber spatula or dough scraper, incorporate butter into dry ingredients, gently stirring and pressing to combine, until a cohesive dough just forms and no dry bits remain, about 1 minute. (Be careful not to overwork the dough.)
Scrape dough into the prepared baking sheet and, using an offset spatula or the flat bottom of a glass or measuring cup, press dough into an even layer. Bake until fragrant and light golden, about 40 minutes.
Remove shortbread from oven and sprinkle top with a 3 tablespoons caster sugar. Using a knife, cut shortbread into individual portions while still warm. Allow shortbread to cool completely in the baking sheet, about 1 hour. Shake excess sugar off individual portions and serve.
