This tender vegetable quiche is packed with produce, including onions, spinach and mushrooms. The Parmesan does double duty, providing cheesiness as well as saltiness. Sliced tomatoes make a lovely topping.
Preheat oven to 400°F. Thaw pie crust for 10 minutes. Lightly prick bottom and sides of the crust with a fork. Bake for 10 minutes. Let cool for 10 minutes.
Reduce oven temperature to 375°F. Place tomato slices on a paper-towel-lined plate and cover with another paper towel. Press gently to remove moisture, keeping the slices intact; set aside.
Heat oil in a large skillet over medium-high heat. Add broccoli, peppers and mushrooms; cook, stirring frequently, until the vegetables are softening and most of the moisture from the mushrooms has evaporated, 6 to 8 minutes. Add spinach and onion; cook, stirring frequently, until the spinach is wilted and the moisture in the pan has evaporated. Spread the vegetables in a single layer on a paper-towel-lined plate to cool slightly, about 5 minutes.
Sprinkle 1/3 cup Parmesan in the bottom of the cooled crust. Whisk eggs, milk and salt in a medium bowl. Gently pat the slightly cooled vegetables dry with another paper towel and spread them in an even layer over the Parmesan in the crust. Sprinkle another 1/3 cup Parmesan over the vegetables. Carefully pour the egg mixture evenly over the top. Gently wiggle the filled crust to allow the contents to settle. Arrange the tomato slices on top and sprinkle with the remaining 1/3 cup Parmesan.
Bake until set, 25 to 30 minutes. Cool slightly before slicing, about 5 minutes. Serve warm or at room temperature.
Cover and refrigerate for up to 5 days. Reheat covered whole quiche at 350°F for 30 to 45 minutes or microwave by the slice.