Slice about 1 inch off the top of each artichoke and trim the stems. Remove the tough outer leaves and trim any sharp, thorny leaf tips with scissors. Put about 2 inches of water in a large pot with garlic and lemon, insert a rack or steamer basket into the pot and bring the water to a boil. Meanwhile, prepare an ice bath.
Place the artichokes on the rack (stem end down) and steam uncovered, until the bottom is tender and the outer leaves can be pulled off easily, about 30 to 40 minutes.
Remove the artichokes with a large spoon and plunge them into the ice bath. Drain and refrigerate until serving time. (Turn the artichokes upside down and leave them upside down in the refrigerator so that all of the water drains from the leaves.).
(The artichokes can be cooked in advance and stored in the refrigerator for up to 2 days.).
In a small bowl, whisk the Champagne vinegar and lemon juice together. Add the herbs & shallots and slowly whisk in the olive oil. Season with salt and pepper to taste.
(The vinaigrette can be made in advance and stored in the refrigerator for up to 5 days.).
Serve the artichokes with a martini glass with a bowl of vinaigrette to dip the leaves inches.