Preheat oven to 325°F.
Arrange the bread on a baking sheet and bake while the oven is preheating for 10 minutes.
Spray a 9-inch square baking dish with cooking spray.
Arrange the bread in an even layer in the baking dish and set aside.
In a medium skillet, heat the oil over medium heat.
Add the leeks and saute until tender, 3 minutes.
Add the broccoli and ¼ cup water, cover and simmer until broccoli is just crisp-tender, 4 minutes.
Arrange the broccoli mixture over the bread in the baking dish.
In a large bowl, whisk together the eggs, milk, salt and nutmeg.
Pour over the bread and broccoli mixture.
Sprinkle with the cheese.
Bake until a knife inserted into the center of the strata comes out clean, 45 minutes to an hour.
