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Heat oven to 350.
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Cut squash in half and lay on baking sheet.
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Bake uncovered for 40 minute.
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Turn squash over, brush with melted butter, and sprinkle with brown sugar.
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Bake 5 minute longer.
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Set aside to cool.
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Season whole chicken breasts with salt and pepper. Let rest.
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Chop carrots, onion, and potatoes into small pieces.
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Cut chicken into bite-size pieces.
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In a Dutch oven, heat oil over medium heat.
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Cook vegetables, except squash, in oil until starting to soften.
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Add chicken and cook over medium heat until chicken is cooked through.
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Sprinkle with cumin and stir.
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Meanwhile, spoon cooled squash out of skin and mash in a bowl.
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Add chicken broth and squash to vegetables and chicken.
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Heat to boiling.
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Reduce heat to low.
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Cover and simmer 20 minutes, stirring occasionally.