1. Preheat oven to 425ºF. Toss asparagus and tomatoes with oil in a shallow baking dish just large enough to hold vegetables in a single layer. Roast, shaking pan halfway through, until asparagus is just tender and tomatoes have wilted, about 12 minutes. Immediately drizzle with vinegar, if desired.
2. Crack eggs over asparagus mixture. Return to oven and roast until egg whites are just set, about 7 minutes. Top with cheese, sprinkle with chives and serve. Offer crusty bread on the side, if desired.