Begin by heating the olive oil in a skillet over medium heat. Add the chopped onion and sauté for about 3-4 minutes until translucent. Toss in the green bell pepper and mushrooms, cooking for an additional 5-7 minutes until the vegetables are tender. Season with a pinch of salt and pepper, then remove from heat.
In a large mixing bowl, whisk together the eggs, whole milk, kosher salt, and freshly ground black pepper until well combined. This will create a creamy custard that envelops the strata.
In the prepared baking dish, layer half of the bread slices on the bottom. Pour half of the egg mixture over the bread, followed by half of the sautéed vegetables and a generous sprinkling of shredded cheddar cheese. Repeat the layers with the remaining bread, egg mixture, vegetables, and cheese.
Cover the baking dish with plastic wrap or aluminum foil and refrigerate overnight. This allows the bread to soak up the egg mixture, resulting in a beautifully custardy texture.
The next morning, preheat your oven to 350°F (175°C). Remove the cover from the baking dish and bake the strata for 45-55 minutes, or until the top is golden brown and a knife inserted in the center comes out clean.
Once baked, let the strata cool for a few minutes. Garnish with minced parsley for a fresh touch before slicing and serving. Enjoy this dish warm, paired with fresh fruit or a side salad for a complete breakfast experience.