Combine 2 cups milk and bread. Cover and chill 30 minutes, stirring occasionally. Remove brown gills from the undersides of portobellos using a spoon; discard gills and stems. Cut mushroom caps in half; cut halves crosswise into 1/2-inch slices.
Preheat oven to 375°.
Heat oil in a large nonstick skillet over medium-high heat until hot. Add portobello and cremini mushrooms, and sauté 4 minutes. Stir in parsley, rosemary, salt, pepper, and garlic; sauté 1 minute.
Combine 1 cup milk, eggs, and egg white, and stir with a whisk. Spoon 2 cups bread mixture into a 2-quart casserole coated with cooking spray. Top with the mushroom mixture; sprinkle with 1/3 cup cheese. Top with remaining bread mixture and 2/3 cup cheese. Pour egg mixture over top. Bake at 375° for 45 minutes or until set.