In a large skillet, heat 1 tablespoon of olive oil over medium heat. Add the peppers and onions, cooking until tender and slightly caramelized, about 8-10 minutes. Stir in garlic and cook for an additional minute. Drain thoroughly and set aside.
Using the same skillet, warm the remaining 2 tablespoons of olive oil. Saute the yellow squash, zucchini, and mushrooms until tender and lightly browned, roughly 8-10 minutes. Drain and pat the vegetables dry to avoid excess moisture in the strata.
Preheat your oven to 325°F and grease a 10-inch springform pan.
In a large mixing bowl, beat the cream cheese, heavy cream, salt, and pepper until smooth. Whisk in the eggs until fully incorporated.
Gently fold the sauteed vegetables, half of the bread cubes, and Swiss cheese into the egg mixture.
Arrange the remaining bread cubes evenly in the bottom of your prepared springform pan. Place the pan on a baking sheet to catch spills, then pour the egg and vegetable mixture over the bread layer.
Bake uncovered for 80-95 minutes, or until the strata is set and a thermometer inserted in the center reads 160°F.
Let the strata cool for 10-15 minutes before removing the sides of the springform pan. Slice into wedges and serve warm.