Cut the Brie half into 6 small wedges, and freeze until completely frozen, about 1 hour.
Meanwhile, tear the bread into small pieces, and put in a small bowl. Add the vinegar, toss and let sit until the bread is very soft, about 5 minutes. Transfer to a food processor. Add the parsley, olive oil, capers, whole cornichons, anchovy, 1/4 teaspoon salt and a few grinds of pepper, and process until a coarse paste. (The salsa verde can be refrigerated for up to 1 day.)
Fill a small pot with about 2 inches of vegetable oil. Clip a deep-fry thermometer onto the side, and bring the oil to 350 degrees F over medium-low heat. Line a plate with paper towels.
Meanwhile, beat the egg in a small bowl. Put the breadcrumbs in another small bowl.
Bread and fry the Brie in two batches: Dip the wedges in the egg, then roll in the breadcrumbs to cover. Repeat for a double breading (make sure there are no bare spots where the cheese peeks through). Being careful of the hot oil, add half the breaded Brie and fry, turning as needed, until a deep golden brown, about 3 minutes. Remove with a slotted spoon, and allow to drain on the paper towels. Repeat with the remaining Brie.
Spoon some of the salsa verde onto 6 small plates. Top each with a wedge of fried Brie, and garnish each with a cornichon half and parsley. Serve hot.
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