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Add the onions to a 5 1/2 quart pot with the olive oil and saute on medium-low heat for 5 minutes, add the garlic and continue cooking for 5 – 7 more minutes until the garlic starts to brown.
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Add the white wine and bouillon cube, mash the bouillon, cook until wine is reduced and syrupy. When the beans are soft, drain them then add them and 4 to 5 cups of water to the onions.
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Stir in the pesto.
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Add the broccoli, salt and pepper and cook for a few minutes until broccoli is just tender.
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You can leave it chunky, puree half or puree the whole batch.
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Top individual bowls with the croutons.