How to Make It
Preheat oven to 375°F. Place potatoes, onion, and 1/2 teaspoon salt in a large microwavable bowl; spray lightly with cooking spray, and toss to coat. Cover with plastic wrap; microwave at high 3 minutes. Heat a 9-inch cast-iron or ovenproof skillet over medium-high. Add 1 tablespoon oil and half of potato mixture; cook, stirring occasionally, until potatoes are almost cooked through, 6 to 8 minutes. Transfer to a rimmed baking sheet. Repeat with 1 tablespoon oil and remaining potato mixture. Let cool 6 minutes.
Whisk together eggs, egg whites, and 1/2 teaspoon salt in a medium bowl. Gently fold in cooled potato mixture, being careful to keep potatoes intact.
Wipe skillet clean. Add 3 tablespoons oil; heat over medium-high 30 seconds. Add potato mixture; press in an even layer. Sprinkle with 3 tablespoons feta; cook until a crust forms on bottom, about 2 minutes. Transfer to oven, and bake at 375°F until golden brown, 20 to 23 minutes.
Whisk together vinegar, lemon juice, honey, remaining 2 tablespoons oil, and remaining 1/8 teaspoon salt in a large bowl. Add spinach, tomatoes, cucumber, and bell pepper; toss to combine. Cut quiche into 8 wedges; top with remaining feta.