Preheat the oven to 375°F. Lightly grease a 9-inch pie dish.
Using a mandoline slicer or vegetable peeler, slice the zucchini lengthwise into very thin ribbons, approximately 1/16-inch thick.
Lay the zucchini ribbons on paper towels and gently blot away excess moisture. If the zucchini is especially watery, sprinkle it lightly with salt, let it sit for about 15 minutes, and then blot it thoroughly.
In a large bowl, whisk together the eggs and heavy cream.
Stir in the mozzarella, Parmesan, garlic, basil, chives, Italian seasoning, salt, black pepper, onion powder, and crushed red pepper flakes, if using.
Roll one zucchini ribbon into a small spiral and place it upright in the center of the prepared pie dish.
Continue wrapping zucchini ribbons around the center spiral, working outward toward the edge of the pie plate. Tuck additional ribbons into any open spaces until the dish is filled and resembles a large zucchini rose.
Slowly pour the egg and cheese mixture over and between the zucchini ribbons. Gently separate a few layers with a butter knife so the mixture can settle between them.
Sprinkle the top with additional Parmesan and lightly mist the zucchini with olive oil spray.
Bake for 40–50 minutes, or until the egg mixture is set in the center and the zucchini edges are lightly golden.
Remove from the oven and allow the pie to rest for 10–15 minutes before slicing.
Garnish with additional fresh basil or chives, if desired. Slice into wedges and serve warm.