Preheat oven to 350 degrees F. Remove edible rind from Brie cheese, if desired, using a vegetable peeler. Cube cheese; set aside.
Split French bread in half horizontally. Hollow out one of the bread halves, leaving a 1/2-inch shell. Place hollowed bread half, cut side up, on a large baking sheet; set aside. (Save remaining bread for another use).
In a medium bowl combine tomatoes, ham, Brie, oil, garlic, and oregano. Toss to combine. Spoon into hollowed bread half. Sprinkle with finely shredded cheese. Bake about 15 minutes or until heated through. Drizzle with vinegar. To serve, cut crosswise into 4 portions. Makes 4 servings.