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Melt 2 Tablespoons of butter in a skillet over medium heat. Add the squash and onions to the pan. Saute for 5 to 7 minutes, until vegetables are tender.
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Remove squash and onions from the skillet and set aside in a large mixing bowl.
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Return the pan to the burner, over medium heat, and melt 1 Tablespoon of butter. Add mushrooms to the pan and sprinkle with garlic powder and onion powder. Sauté for 5 minutes, until soft and brown.
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In a measuring cup, combine flour, half the broth, salt and pepper. Stir until well smooth and pour over the mushroom mixture. Add the remaining chicken broth and bring to a boil.
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Cook for 2 minutes, whisking or stirring constantly, to avoid clumping, until the mixture has thickened.
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Reduce the heat to low and add the half-and-half. Stir to fully incorporate. Simmer for 10-15 minutes, stirring frequently to ensure the soup mixture remains smooth and creamy.
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Remove the mushroom soup mixture from the heat and set aside to cool slightly.
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Grease an oblong, shallow, 2-quart baking dish with butter or cooking spray. Preheat oven to 350 degrees.
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Add herbed stuffing mixture and 4 Tablespoons of melted butter to the bowl with the squash and onion mixture. Stir until the stuffing mixture is moistened
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Finally, add in the homemade cream of mushroom soup and stir until fully incorporated.
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Spread the squash, stuffing and soup mixture into the baking dish. Bake for 30 to 40 minutes at 350 degrees, until heated through but not dried out.