Wash and halve the tomatoes. Wash the asparagus, cut off the woody ends. If necessary, cut the stalks in half lengthwise. Peel and finely chop the onions.
Heat 3-4 tablespoons of oil in a large frying pan. Fry the asparagus for 5-8 minutes in portions, remove and season with salt and pepper. Fry the tomatoes and onions in the hot frying fat. Season with salt, pepper and 1 tsp. sugar. Remove from heat.
Stir in vinegar and 4 tablespoons of oil. Chop the capers coarsely and mix in with the olives. Season to taste. Pour everything over the asparagus. Wash parsley, shake dry, pluck leaves and chop roughly. Sprinkle over the salad. Serve with Parma ham.
Time saver, watch out: Asparagus and tomato stock can chill in the fridge overnight together. It's best not to mix them until the next day, because the acidity in the tomatoes will cause the stalks to lose their bright green colour.