In a bowl, whisk the eggs and water. Melt 2 tablespoons of the butter in a large stainless steel bowl set over a pot of simmering water. Add the eggs and cook over low heat, gently stirring with a heatproof rubber spatula and scraping the bottom of the bowl until the eggs just begin to set, about 5 minutes. Add the remaining butter to the eggs, 1 piece at a time, and cook, stirring and scraping the bottom and sides of the bowl, until the eggs are thick and cooked through but still soft, about 5 minutes longer. Season with salt and pepper; transfer to plates. Drizzle with the truffle oil, sprinkle with the chives and serve at once with the brioche.