Preheat your oven to 400°F. While it heats, lightly coat a 9-inch pie dish with olive oil, making sure to cover the bottom and sides evenly. This prevents sticking and helps the quiche release cleanly after baking.
While the oven preheats, prepare all your vegetables: peel the zucchini into thin ribbons using a vegetable peeler or mandoline, halve the grape tomatoes, and chop the fresh basil. I find it helpful to keep the zucchini ribbons on a paper towel to remove excess moisture—this prevents the quiche from becoming watery during baking.
In a large bowl, whisk together the eggs and milk until well combined and slightly frothy. Add the salt, pepper, garlic powder, and red pepper flakes, whisking until the seasonings are evenly distributed. This creates a smooth, well-seasoned custard that will cook into a tender quiche.
Pour the egg custard mixture from Step 3 into the prepared pie dish. Gently arrange the zucchini ribbons from Step 2 on top, distributing them evenly so they distribute the vegetables throughout the quiche rather than clumping in one area. Scatter the halved tomatoes and chopped basil over the surface, then sprinkle the grated parmesan cheese on top. I like to press the vegetables down slightly so they stay submerged during baking.
Place the quiche in the preheated 400°F oven and bake for 30 minutes, until the eggs are set but still slightly jiggly in the very center, and the top is golden brown. The quiche will continue to cook slightly as it cools, so don't overbake or it will become tough and rubbery.
Remove the quiche from the oven and let it rest for 5-10 minutes before slicing. This allows the custard to set fully and makes it easier to cut clean slices. Serve warm or at room temperature.