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Add the onion and shallot to a 5 1/2 quart pot and add 2 tablespoons of olive oil. Saute on medium-low heat until the onions are fairly soft. (about 5 minutes)
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Add the garlic and saute until the garlic just becomes lightly golden.
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While onions are cooking, wash the leek really well, there is always dirt on the inside of the leaves. Cut into quarters after you wash it and thinly slice.
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When the garlic is lightly golden, add the bouillon cubes and wine then mash the bouillon and reduce to a syrup. (about 2 -3 minutes)
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Add the leeks to the onions when the wine is reduced and continue sauteing until the leek is soft. (about 3 - 5 minutes)
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Dice the potatoes and put in a bowl of water.
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Drain the potatoes and add to the leeks along with the water, thyme, tarragon, rosemary, bay leaf, salt and pepper.
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Turn the heat to high and bring to a boil then reduce heat to medium and simmer until the potatoes are very soft (about 40 minutes)
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In a separate saute pan add carrots, 2 tablespoons of wine, 2 tablespoons of water, a dash of olive oil, a dash of salt and pepper. Simmer on medium heat covered until they are soft and the liquid reduces. It can happen fast, so make sure to check on them (about 5 minutes). Add a tablespoon olive oil to deglaze. Set aside.
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Puree a third of the soup in a food processor or with an immersion blender, pour back into the pot and add the carrots. Cook for a couple of minutes to reheat the carrots.