Boil water in steamer or large saucepan over high heat. Reduce heat to medium-high. Place broccoli in steamer basket; cook for 3 to 4 minutes, or until tender-crisp and bright green. Place in ice water bath to stop cooking process. Drain and coarsely chop. Set aside.
Preheat oven to 350º F.
Heat oil in a medium nonstick skillet over medium heat.
Add onion; cook, stirring frequently, for 4 to 6 minutes, or until onion is translucent.
Add garlic; cook, stirring frequently, for 1 minute. Remove from heat. Set aside.
Combine eggs, milk, spinach, salt, pepper, broccoli, and onion mixture in a large bowl; mix well.
Place bread and cheese in 3-quart baking dish that has been lightly coated with spray.
Top with egg mixture. Press down gently so that bread absorbs egg mixture. Cover with aluminum foil.
Bake for20 minutes. Remove foil; bake for an additional 15 to 25 minutes, or until strata has puffed up, is cooked through, and is lightly browned on top.
Tip: Strata can be covered and refrigerated overnight before baking. (This may increase baking time.) This works well if you are serving it for brunch.