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Place soup pouches in microwave-safe dish. Cut small slit in top of each pouch to vent. Heat 5 minutes on high power. Cut each pouch open and pour soup into large bowl; set aside.
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Melt butter in small skillet over medium-high heat. Saute shallots and shiitake mushrooms until soft; set aside.
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Stir half and half, eggs, parsley and half of cheese mixture into bowl of soup; set aside.
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Spray 9x13-inch baking dish with cooking spray; layer half of bread cubes on bottom. Arrange red peppers, chicken and shiitake mixture over bread cubes. Layer remaining half of cheese mixture over; and add remaining bread cubes over the top.
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Pour soup mixture over, cover with foil. (Can be made a day ahead, covered and refrigerated.) Bake in a preheated 350 F oven for 30 minutes. Remove foil and bake until top is golden brown (10 to 15 minutes).