Place a rack in the center of your oven and preheat to 350°F. Coat a 9-inch deep pie dish with nonstick spray.
In a large bowl, whisk together the all-purpose flour, white whole wheat flour, baking powder, thyme, pepper, and salt. Whisk in the eggs until evenly combined. The mixture will be very thick.
In a medium skillet, melt the butter over medium heat. Add the onion. Sauté until the onion is softened and browning in places, about 10 minutes. Let cool for a few minutes, then transfer to the bowl with the flour mixture.
To the bowl with the egg mixture, add the zucchini, cheddar, and ¼ cup of the Parmesan. Fold to combine, distributing the ingredients as evenly as you can.
Transfer the mixture to the prepared pie dish, using a spatula to smooth the zucchini slices into an even layer. Sprinkle the remaining 2 tablespoons Parmesan over the top.
Bake zucchini pie until it is cooked through, puffed and golden brown on top, and a butter knife inserted in the center reveals that it is set, 30 to 40 minutes. Garnish with fresh basil. Let cool for 10 minutes before slicing and serving. Enjoy warm or at room temperature.
Notes
TO STORE: Wrap leftovers in the pie dish or transfer them to an airtight container. Refrigerate for up to 4 days.
TO REHEAT: Warm up the zucchini pie in the microwave or in a 350ºF oven until it's heated through. You can also take out a slice and let it come to room temperature or eat it cold.
TO FREEZE: Freeze this recipe in an airtight container for up to 3 months. Thaw it in the refrigerator before reheating.