Line a 9x13-inch baking pan with parchment paper, leaving extra overhang on the sides for easy removal. Spray with nonstick cooking spray.
In a medium saucepan, melt the butter over medium-low heat. As the butter melts, it’ll start to foam, then turn a clear golden color. Continue to stir the butter, scraping up any browned specks from the bottom of the pan as it starts to brown. It should have a nutty aroma.
Once browned and nutty, remove from the heat and pour into a shallow dish. Chill butter in freezer until solid, about 45 minutes.
Preheat the oven to 350ºF. Use a spoon to scrape the now solidified butter out of the dish and into the bowl of a stand mixer fitted with a paddle attachment. Beat butter on high until creamy. Add both sugars, lemon zest, orange zest, vanilla and salt, and continue beating until blended. Slowly beat in the flour.*
Press dough into the bottom of the prepared pan and bake for 10-12 minutes.
While crust is baking, prepare the filling by whisking the eggs, granulated sugar, powdered sugar, zest, and salt together in a large bowl. Whisk in the lemon juice and orange juice, and then the flour, until combined. Remove the parbaked crust from the oven. Pour the lemon filling onto the warm crust.
Reduce oven temperature to 325ºF, and bake for 25-30 minutes, or until center is set. Place pan onto a wire rack to cool completely before covering and transferring to the refrigerator until chilled.
Using a sharp knife dipped in hot water and wiped dry, cut lemon bars into squares and dust with powdered sugar just before serving.