In 10-inch nonstick skillet, heat oil over medium heat. Add bell pepper, onion and garlic; cook about 6 minutes, stirring occasionally, until tender. Remove from heat. Stir in artichokes and spinach; set aside.
Spray 13x9-inch (3-quart) glass baking dish with cooking spray. Arrange bread cubes in dish. Spoon vegetable mixture evenly over bread cubes; sprinkle with Monterey Jack cheese.
In medium bowl, beat eggs, milk, mustard, salt and pepper with wire whisk until blended; pour evenly over bread, vegetables and cheese. Sprinkle with Parmesan cheese. Cover tightly with foil; refrigerate at least 4 hours but no longer than 24 hours.
Heat oven to 350°F. Bake covered 30 minutes. Uncover; bake 20 to 30 minutes longer or until top is golden brown and knife inserted in center comes out clean. Let stand 10 minutes before cutting.