Put the eggs in a large saucepan and cover with cold water by 1 inch. Bring to a boil, then reduce the heat and gently simmer 10 minutes. Fill a large bowl with ice water. Drain the eggs and transfer to the ice water; let cool 5 minutes. Peel and chop the eggs and transfer to another large bowl.
Meanwhile, toast the curry powder in a small dry skillet over low heat, stirring often, about 1 minute. Let cool. Sprinkle over the eggs and add the mayonnaise, mustard, 1/2 teaspoon salt and a few grinds of pepper. Gently stir to combine. Stir in the chopped celery and chives.
Top the bread with the lettuce leaves, then the egg salad, radishes and sprouts; sprinkle with the celery leaves and more chives. Serve with the beets.