In a large skillet, heat olive oil over medium heat. Add diced sweet red and yellow peppers along with chopped red onion, cooking for about 5-7 minutes until tender. Stir in minced garlic and cook for an additional minute, then drain mixture and set aside.

Using the same skillet, add more olive oil if necessary and sauté yellow summer squash, zucchini, and fresh mushrooms over medium heat for 4-6 minutes until tender and golden color is achieved. Drain and set aside with the first mixture.

Preheat your oven to 325°F (160°C). This temperature is crucial for an even bake.

In a mixing bowl, combine softened cream cheese, heavy whipping cream, salt, and pepper. Beat until smooth and creamy, then whisk in eggs until incorporated. Fold in sautéed vegetables, half of the cubed bread, and shredded Swiss cheese.

Grease a 10-inch springform pan with olive oil and layer remaining bread cubes. Pour prepared filling over bread, ensuring even coverage.

Place the assembled strata on a baking sheet and bake uncovered for 80-95 minutes until puffed and golden-brown. Allow to cool for 10-15 minutes before slicing.