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Turn oven to the broil setting and place the bell peppers cut side down and broil until the skins are charred and blackened, about 10 minutes.
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Remove the peppers from the oven and set aside to let cool.
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Meanwhile, heat the olive oil in a large sauce pot, add the onion and cauliflower pieces. Cover the pot and let cook until the cauliflower is fork tender, about 10-12 minutes.
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Remove the charred skin from the peppers and loose chop them.
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Working in batches, blend the cauliflower/onion mixture on high in a food processor, until fully pureed and smooth. Add about 4 cups of the chicken stock gradually while you're pureeing these batches.
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Set each batch load aside in a bowl or separate pan, don't add back to the original pot.
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Puree the bell peppers as well, adding chicken stock as necessary. The total amount of stock while blending the cauliflower mixture and bell peppers should not exceed 4 cups.
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Meanwhile, add a little more olive oil to the empty sauce pot (same one you were using for the caulifloweand add the pancetta. Cook for about 2 minutes until just browned.
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Add the garlic and thyme. Cook for about a minute until fragrant, about a minute.
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Pour in the cauliflower and red pepper puree. Stir in the heavy cream, paprika, cayenne, and 2-3 cups of chicken stock, adjusting to desired consistency.
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Bring the soup to a simmer and cook covered for about 20 minutes.
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During the last 5 minutes of cooking, add 5 oz. of the crumbled goat cheese, reserving 3 oz. for garnishing.
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Ladle into bowls and garnish with the extra goat cheese and paprika.