Place the bread on a baking sheet and cook, stirring once or twice, for 10 – 15 minutes or until the bread is lightly toasted. Let cool. Leave the oven on.
Butter a 9- by 12-inch (or similar) casserole dish generously with the softened butter.
Whisk the eggs and egg yolks with the half-and-half, mustard, salt, pepper, and nutmeg.
Combine the bread with the ham and 1½ cups gruyere cheese and spread evenly into the prepared casserole dish. Pour the egg mixture over the top, and gently press the bread down so that all the liquid covers the bread. Let sit for 15 minutes. Bake for 45 minutes or until the custard looks set.
Turn on the broiler. Combine the remaining ½ cup gruyere cheese with the Parmesan cheese and sprinkle over the top. Broil for 1 – 2 minutes or until the cheeses melt. Let cool a few minutes before serving. Top with chives if desired.