Set up a steamer basket and steam the eggs, covered, for 9 minutes. Meanwhile, set up an ice bath by filling a large bowl with about 4 cups combined ice and water. Once eggs are cooked, transfer them immediately to the ice bath. When completely cooled, peel eggs.
Chop the eggs roughly and transfer to a large bowl. Add minced chives and chopped dill. Add 1 cup mayonnaise and mix. Taste. Add remaining mayonnaise if desired.
Keep refrigerated until it’s time to serve, then top with cured trout roe.