Place the eggs in a large saucepan or pot so that they sit in a single layer. Add enough cold water to cover the eggs by 1 inch. Bring to a boil uncovered over high heat. Remove from the heat, cover with a lid, and let sit for 10 minutes.
Meanwhile, mix the yogurt, mayonnaise, cumin, salt, coriander, turmeric, and pepper together in a medium bowl until smooth. Prepare an ice bath (large bowl filled with ice water).
When the eggs are ready, tap them gently against the counter to crack the shell in a few places, then submerge in ice water for at least 1 minute. Peel the eggs and dice into small pieces. Fold the eggs into the yogurt mixture. Taste and season with more salt as needed.
Place the naan on a cutting board. Divide the arugula over the naan. Dollop the egg salad over the arugula, spread into an even layer, and top with cilantro if using. Cut each naan into wedges and serve.