In a skillet, heat olive oil over medium heat. Add onions and bell pepper, sauté until softened.
Add spinach and cook until wilted.
In a greased 9×13-inch baking dish, layer half the bread cubes, followed by half of the vegetable mixture and half of each type of cheese. Repeat layers.
In a bowl, whisk together eggs, milk, salt, pepper, and mustard. Pour this mixture evenly over the layered bread.
Cover the dish and refrigerate for at least an hour or overnight to allow the bread to absorb the egg mixture.
Preheat oven to 350°F. Bake the strata for 50-60 minutes until the top is golden and the center is set.
Allow to rest for a few minutes after removing from the oven. Garnish with fresh parsley when serving.