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melt the butter in a large dutch oven or pot over low heat.
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add the onion, broccoli and carrots and cook until tender, about 5 minutes.
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stir the flour and cook until dissolved, then gradually stir in the half-and-half and turn heat to medium.
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Bring to a simmer, stirring the veggies
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add the chicken broth, bay leaves and nutmeg, then season with salt and pepper and bring to a simmer.
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reduce the heat to medium-low and cook, uncovered, until thickened, about 20 minutes.
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meanwhile, prepare the bread bowls:
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using a sharp knife, cut a circle into the top of each loaf, leaving a 1-inch border all around.
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remove the bread top, then hollow out the middle with a fork or your fingers, leaving a thick bread shell.
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discard the bay leaves.
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puree the soup in batches in a blender until smooth; you'll still have flecks of carrot and broccoli.
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return to the pot. (or puree the soup in the pot with an immersion blender.)
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add the cheese to the soup and whisk over medium heat until melted.
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add up to 3/4 cup water if the soup is too thick.
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ladle into the bread bowls and garnish with cheese.