Preheat oven to 350 degrees F. Coat a 9-inch deep-dish glass pie pan with cooking spray.

Cook sausage in a large nonstick skillet over medium-high heat, breaking it up into small pieces with a wooden spoon, until cooked through, about 5 minutes. Transfer to a medium bowl lined with paper towels. Coat the pan with cooking spray, add onion and mushrooms and cook, stirring, until beginning to brown, 4 to 5 minutes. Add spinach and stir until just wilted, about 1 minute. Transfer the vegetables to the bowl with the sausage; set aside.

Whisk eggs, egg whites, milk and pepper in a medium bowl.

Unroll phyllo onto a clean, dry surface. Cover with a sheet of wax paper and then a damp kitchen towel. Place one sheet of dough into the prepared pie pan, spray with cooking spray and sprinkle lightly with breadcrumbs. Repeat with the remaining phyllo, spraying and sprinkling between each layer, turning each sheet at a 45 degrees angle to cover the entire pan. Trim the phyllo edge with kitchen shears to be level with the rim of the pan. Spread the sausage mixture in an even layer on top of the phyllo; pour in the egg mixture and top with cheese.

Bake the quiche until the top is browned and the phyllo is crispy, 40 to 45 minutes. Let cool for 10 minutes before cutting into wedges.

MAKE AHEAD TIP: Timing tip: Thaw frozen phyllo in the refrigerator for at least 8 hours or overnight before preparing the recipe.