Reserve and refrigerate 6 center slices from eggs for garnish. Chop remaining eggs.
Combine chopped eggs, avocados, tomato, onion and parsley in large bowl; Toss gently to mix. Add dressing and stir gently just until ingredients are evenly coated with dressing.
Refrigerate at least 1 hour to blend flavors. Serve on spinach leaves, topped with reserved egg slices.
To hard-boil eggs:
Place eggs in saucepan large enough to hold them in single layer. Add cold water to cover eggs by 1 inch. Heat over high heat just to boiling.
Remove from burner. Cover pan. Let eggs stand in hot water about 15 minutes for large eggs (12 minutes for medium eggs; 18 minutes for extra-large eggs).
Drain immediately. Cool completely under cold running water or in bowl of ice water, then refrigerate.
Hard-boiled eggs are easiest to peel right after cooling. Cooling causes the egg to contract slightly in the shell.