Squeeze the lemon into a bowl of cold water; add the halves to the bowl. Trim 1 inch off the stem ends of the artichokes. Using a sharp stainless steel knife, halve the artichokes crosswise. Pull off all of the green outer leaves until you reach the yellow leaves. Peel the tough skin off the bottoms and stems. With a teaspoon, scrape out the hairy chokes. Add the artichokes to the bowl of lemon water as they are trimmed.
In a medium saucepan, combine the stock with the olive oil, wine, thyme sprigs, shallot and garlic. Add the artichokes and season lightly with salt and pepper. Bring to a simmer and cook over low heat until the artichokes are very tender, about 40 minutes. Remove and discard the thyme sprigs.
Working in batches, transfer the contents of the saucepan to a blender and puree until completely smooth. Transfer the soup to a bowl and let cool, then refrigerate until thoroughly chilled.
Just before serving, stir the milk and cream into the soup and season with salt and pepper. Ladle the soup into shallow bowls and serve the Mushroom Toasts on the side.
The soup can be prepared through Step 3 and refrigerated, covered, for up to 2 days.
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