Step 1With a sharp knife, trim the artichokes so that they stand on flat bottoms, and cut off about 2 inches from the tops. With scissors, trim the sharp tips off the leaves. Cook submerged in a large pot of boiling water until the bottoms are easy to pierce with a fork and you can pull out a leaf, about 20 to 23 minutes. Place the artichokes in a bowl of ice water to stop the cooking process.
Step 2When cool enough to handle, remove the small sharp leaves from the center of the artichoke and use a spoon to scoop out the inner choke. Discard.
Step 3Place about one-fourth of the Brie into the hollowed-out center of each artichoke and disperse the rest of the cheese between the layers of leaves.
Step 4Heat the oven to 350 degrees. Place the artichokes standing up on a baking sheet, and bake until the Brie is melted, about 10 minutes.
Step 5While the artichokes are baking, combine the shallots and white wine in a saucepan over high heat. Add the butter, a few pieces at a time, whisking between additions until all the butter has been incorporated. Remove from heat, and whisk in the mustard, white wine vinegar, lemon juice and salt and pepper.
Step 6Place the artichokes on a serving platter, drizzle the wine sauce over and place in the center of the table so that diners can tear off leaves with melted Brie and dip into the pooled sauce.