In a large skillet, saute peppers and onion in 1 tablespoon oil until tender. Add garlic; cook 1 minute longer. Drain; pat dry and set aside. In the same skillet, saute the yellow squash, zucchini and mushrooms in remaining 2 tablespoons oil until tender. Drain; pat dry and set aside.
Preheat oven to 325°. In a large bowl, beat cream cheese, cream, salt and pepper until smooth. Beat in eggs. Stir in vegetables, half of the bread cubes and Swiss cheese. Arrange the remaining bread cubes in a greased 10-in. springform pan. Place on a baking sheet. Pour egg mixture into pan.
Bake, uncovered, until set and a thermometer reads 160°, 80-95 minutes. Let stand for 10-15 minutes before serving. Run a knife around edge of pan to loosen; remove sides. Cut into wedges.