Place the eggs in a single layer in a saucepan and cover with cold water by about 1 inch.
Bring the water to a full boil over high heat. As soon as it boils, remove the pan from the heat, cover it and let the eggs sit for 12 minutes.
Drain the eggs and transfer them to a bowl of ice water. Let them cool completely, about 10 minutes, then peel.
Make the sandwiches
Chop the boiled eggs with a fork, an egg slicer or a knife, leaving some small pieces of white and yolk.
In a bowl, combine the eggs, mayonnaise, chopped pickle and chopped ham. Stir gently until everything is coated.
Taste, then season with salt and pepper. Ham and pickles are salty, so you may not need much salt.
Spread the ham and egg salad over 2 slices of bread, add a little cilantro if you like, and top with the remaining bread. Cut in half and serve.
Notes
Boiled eggs: older eggs peel more easily than very fresh ones. Boiled eggs keep in the shell in the fridge for about a week, so you can make them ahead.Storing: keep the ham and egg salad in an airtight container in the refrigerator for up to 3 days. Egg salad doesn't freeze well. Build the sandwiches right before serving so the bread doesn't get soggy.For a twist, add in paprika or ground mustard to amp up the flavor.