To pickle onions, combine onion and vinegar in a small bowl. Cover and let stand at room temperate for at least 30 minutes or in the refrigerator for up to 24 hours.
Pre-heat oven to 400 °F. On a baking sheet lined with parchment paper, place the trimmed asparagus in a single layer. Drizzle asparagus spears with 1 tablespoon olive oil. Roast asparagus for 15-20 minutes (until tender crisp).
Meanwhile, in a large bowl combine arugula and mint. Use a slotted spoon to transfer the onions to the mixture. Pour 3 tablespoons of the vinegar from the onion bowl into a small screw top jar. Add remaining oil, salt and pepper. Cover and shake well.
Add cooled asparagus spears to the salad and drizzle vinegar mixture over the salad, toss gently to coat. Serve immediately
Note: If you have thin asparagus spears, leave them whole. If the spears are thick, cut them into 1 inch chunks.