1. Preheat the oven to 375°F.
2. Steam the broccoli until tender, about 5 minutes. Coarsely chop and set aside.
3. Lightly oil or coat a 9-inch pie plate with nonstick cooking spray. Sprinkle the bottom and sides with the bread crumbs. Arrange the broccoli, ham, and mozzarella cheese over the bottom of the pie plate.
4. Whisk together the eggs, milk, salt, thyme, and pepper in a medium bowl. Pour the egg mixture over the broccoli and top with the Parmesan cheese.
5. Bake uncovered until golden brown, 35 to 40 minutes