Wash and then steam the artichokes until tender--about 20-30 minutes. Pull off and save 32 perfect leaves. Clean and remove the artichoke bottom. Use the rest of the artichoke for other recipes.
For the garlic beurre blanc, bring the wine and vinegar to a boil in a skillet. Lower the heat to almost nothing and add the heavy cream. Puree the garlic (don't use a garlic press), and add to the pan. Slowly whisk in the softened butter, then add salt and pepper to taste. Remove from heat and reserve.
Heat one-third of the clarified butter in a skillet over medium-high heat. Sauté the sea scallops until lightly browned, but still bulging--about a minute and a half per side. Add more butter to the pan as necessary to complete the cooking.
Combine all the ingredients for the vinaigrette, whisking the oil slowly into the other ingredients.
Place an artichoke bottom on each plate. Surround it with eight artichoke leaves. Drizzle some vinaigrette over the artichokes. Divide the scallops among the four plates, and spoon 2 Tbs. garlic beurre blanc over each. Garnish with diced tomato.
