Cook asparagus in large pot of boiling salted water until just tender, about 5 minutes. Drain. Refresh under cold running water and drain thoroughly. Arrange asparagus on large platter. Cover and refrigerate until cold.
Whisk oil and vinegar to blend in small bowl. Add tomato, bell pepper, green onion and parsley. Season with salt and pepper. (Can be prepared 3 hours ahead. Let stand at room temperature.)
Spoon half of vinaigrette over asparagus. Garnish with egg. Pass remaining dressing separately.
