Preheat oven to 400 degrees F. Cut squash in half, scoop out the seeds and place cut side down on a baking sheet lined with parchment paper. Poke skin randomly with a fork and bake for 30 minutes. Remove from the oven and set aside to cool until safe to handle.
Using a fork, separate spaghetti squash into strands and add to a medium bowl. Sprinkle with 1/4 teaspoon salt and mix. Using your hands, squeeze out liquid a bit. Return to the bowl along with 1/2 teaspoon dried basil and 1/2 teaspoon garlic powder and mix to combine.
Spray deep pie dish with cooking spray and transfer squash mixture into it. Using your hands, press evenly on the bottom and sides. Set aside.
Preheat ceramic non-stick skillet on medium heat and swirl oil to coat. Add onion and bell pepper; sauté for 5 minutes or until golden brown, stirring occasionally.
Meanwhile in a large bowl, add eggs, balsamic vinegar, 1 teaspoon dried basil and 1/4 tsp salt and whisk. Add cheddar cheese, feta cheese, sauteed onion and bell pepper, and fresh zucchini, broccoli, cauliflower and tomatoes. Stir well to combine.
Pour mixture into prepared crust and level with spatula. Bake for 50 minutes or until the knife inserted in the center comes out clean.
Let quiche cool down for at least 30 minutes. Cut into 8 slices and serve hot or cold.
Notes
Store: Refrigerate in an airtight container for up to 3 - 4 days. Do not freeze.