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Melt butter over medium heat and add the vegetables; stir to coat.
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Reduce heat to very low, cover and cook the veggies, stirring occasionally, for 30 to 40 minutes.
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Add chicken broth. Increase heat to medium, cover and simmer 45 minutes, until veggies are utterly tender.
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In batches, puree soup in blender or food processor.
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Return soup to pot; add 1 to 1 and ½ C milk or light cream, thinning to desired consistency.
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Season to taste with salt and pepper.