Preheat oven to 375 degrees F.
Unroll the pie crust and place it in a 9-inch pie plate, pressing gently into the corners. If you like, crimp the edges.
Bring a medium pot of salted water to a boil over high heat. Add the broccoli florets and cook for 1 minute. Drain in a colander and rinse with very cold water or immediately plunge into a bowl of ice water. Arrange the broccoli on the bottom of the pie crust.
In a large bowl, combine the eggs, egg whites, water, cottage cheese, thyme, salt and pepper. Whisk vigorously to break up the cottage cheese.
Pour the egg mixture over the broccoli in the pie dish. Top with the Cheddar cheese.
Bake until the egg is just set and a small, sharp knife inserted in the center comes out clean, 30 to 40 minutes.
Let the quiche rest for 5 minutes, then cut into 6 wedges. Serve.