Spray a 9x13-inch baking pan with cooking spray. Set aside. Preheat oven to 350ºF.
Heat the oil in a large skillet over medium heat. Add in the onion and red pepper flakes. Sauté for 4-5 minutes, or until tender. Stir in the asparagus and cook for 2-3 minutes. Add in the swiss chard leaves and cook until wilted, 2-3 minutes. Season to taste with salt and black pepper. Set aside.
In a large bowl, whisk together the eggs and milk. Season to taste with salt and black pepper. Set aside.
Place half of the bread cubes in the prepared baking dish. Top with half of the veggies and half of the cheese. Repeat with remaining bread, veggies, and cheese.
Pour the egg mixture over the bread, veggies, and cheese. Press down with a spatula to make sure all of the bread cubes get soaked. Do this every 5 minutes for 15 minutes.
Bake, uncovered, for 45-50 minutes or until golden brown and set. Let cool for 5 minutes before serving.