Place a rack in the center of your oven and preheat the oven to 350 degrees F. Line an 8x8-inch pan with parchment paper and set aside.
In a small microwave-safe bowl, melt the butter. In a medium mixing bowl, stir together the all-purpose flour, whole wheat pastry flour, 1/4 cup powdered sugar, and 1/8 teaspoon kosher salt. Pour the butter over the top and stir to combine. The batter will be very wet. Press into an even layer in the prepared pan, building the crust 1/2 inch up the sides all around. Bake the crust for 15 to 20 minutes, until barely light brown. Leave the oven at 350 degrees F.
While the crust bakes, in a large mixing bowl or the bowl of a stand mixer fitted with the paddle attachment, rub the granulated sugar and lemon zest together with your fingers until moist and fragrant. Add the eggs, lemon juice, baking powder, and remaining 1/4 teaspoon salt. With an electric mixer, beat on high speed until light and well blended, about 3 minutes. Pour into the hot crust (no need for it to cool).
Return to the pan to the oven and bake 25 to 30 minutes, until the bars are set, no indentation remains when you touch the center with your finger, and your kitchen smells incredible. Let cool completely, then dust with powdered sugar. Cut into squares and serve.
Notes
TO STORE. Lemon bars may be stored for up to 1 day at room temperature. Beyond that, lemon bars should be stored in an airtight container in the refrigerator for up to 1 week.
TO FREEZE. Once cooled, cut the lemon bars into squares and then wrap individually in foil or plastic and store in an airtight container for up to 3 months.
TO THAW. Transfer frozen bars to the refrigerator and let thaw overnight.