Peel the hard-boiled eggs and slice in half lengthwise.
Preheat oven to 350 degrees F. Set the oven rack in the middle position of your oven.
Butter a 9x13-pan, a flat casserole dish that will hold at least 2 quarts, or enough individual Gratin dishes to hold the eggs
Arrange the peeled and halved eggs cut-side-down in the buttered casserole dish.
Melt the 2 tablespoons butter. Combine with the 1/2 cup bread crumbs. Set aside.
Combine the cornstarch with the 1/4 cup water. Mix to form a smooth paste. Set aside.
Heat the half and half or cream in a saucepan set over a medium flame. When the liquid begins to bubble, add the cornstarch mixture. Whisk continuously for one minute while the sauce boils.
Remove from heat. Stir in the Swiss cheese, mustard, nutmeg - if using, and the salt. Pour the bechamel evenly over the eggs; top with the buttered bread crumbs. Sprinkle with paprika.
Bake at 350 degrees for 25-30 minutes - until the gratin bubbles and the top turns golden brown.
Serve hot.