Place the bread in a large bowl. Heat the oil in a large skillet over medium heat. Add the shallots and cook 1-2 minutes until tender. Add the mushrooms and cook, 3-4 minutes until they start to soften. Add the spinach and stir to combine. Season the mixture with the thyme, ½ teaspoon salt and ¼ teaspoon pepper. Transfer the mixture to the bowl with the bread and mix the ingredients together.

Whisk the eggs, milk, mustard, ½ teaspoon salt, ¼ teaspoon pepper and about ¾ of the cheese together in another bowl.

Spray a 8x12-inch baking dish with cooking spray. Transfer the bread and vegetable mixture to the dish, spreading it out evenly. Pour the egg mixture over the top and gently press the bread down into the liquid. Sprinkle the remaining cheese on top. Alternatively, to make individual portions, divide the mixture between the cups of a muffin pan (it will make about 16 portions so you may need two pans).

Let the mixture sit while you preheat the oven to 350 degrees F. Alternatively, the dish can be prepared the night before and allowed to soak in the refrigerator overnight.

Bake strata in the oven uncovered for 50-60 minutes (30-40 minutes if using a muffin pan) until it is puffed up and golden brown. Cut into pieces and serve.