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3 cups unsalted chicken stock
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1 3/4 cups broccoli florets, coarsely chopped (about 8 ounces)
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1 cup diced yellow onion
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1/2 cup chopped carrot
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3/8 teaspoon salt
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1/4 teaspoon freshly ground black pepper
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2 garlic cloves, minced
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3/4 cup half-and-half
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4 ounces shredded reduced-fat extra-sharp cheddar cheese, divided
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1/4 cup fresh flat-leaf parsley leaves
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