Add the garlic and sauté for 1 minute more. Add the potatoes and the broth. Bring to a boil, then reduce the heat and simmer for 15 to 20 minutes, or until the potatoes are tender. Stir in the artichokes.
Let cool slightly, then transfer half of the soup to a blender, along with the cashews, mustard, capers, and 1 tablespoon of the lemon juice. Puree until smooth, and then pour the mixture back into the soup pot. Stir in the water as needed to reach your desired consistency. (I love a super thick soup, so I used closer to 1/2 cup.) Add the dill, chives, and remaining 2 tablespoons lemon juice. Season to taste with salt and pepper.
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