Preheat the oven to 350 degrees F. Spray a 9×13 pan with cooking spray. Heat a large skillet over medium heat. Add the veggies except the spinach and saute until soft, about 6 minutes. Add the spinach and garlic and saute another 5 minutes. Stir in the thyme and nutmeg and season with salt and pepper. Remove from heat.
place half the bread cubes in the bottom of the baking dish and top with half the vegetable mixture and half the cheese. Repeat with the remaining bread, veggies and cheese.
In a large bowl or measuring cup whisk together the eggs and milk. Season with salt and pepper and slowly pour over the bread mixture. Press down to help the bread soak up the egg mixture. Do this every 10 minutes for 30 minutes or leave it sit overnight.
Bake uncovered for 45-60 minutes or until golden brown and set.