Preheat the oven to 400 degrees F. Heat the olive oil in a medium nonstick skillet over medium heat. Add the onion and thyme sprigs, season with salt and pepper and cook, stirring occasionally, until the onion is caramelized, 15 to 17 minutes (reduce the heat if the onion is getting too dark). Add the Worcestershire sauce and cook until the skillet is dry, about 1 minute. Add the beef broth and cook, stirring, until the mixture is slightly saucy, 2 to 3 minutes. Remove from the heat and let cool slightly; discard the thyme sprigs and stir in the chives.
Using a small serrated knife, hollow out the bread loaf, leaving a ½-inch-thick shell; reserve the cut-out bread. Drizzle the inside of the bread with olive oil and season with salt and pepper. Fill the loaf with half of the brie, then top with the onion mixture and the remaining brie; transfer to a baking sheet. Bake until the brie melts and the bread is toasted, about 15 minutes.
Meanwhile, slice the reserved bread into pieces and arrange on a separate baking sheet; drizzle with olive oil and season with salt and pepper. Bake until toasted, 5 to 8 minutes. Top the dip with more chives and serve with the toasted bread and crackers and/or crudites.