In a large mixing bowl, whisk together the eggs, cream and milk. Set the egg-cream mixture aside while you prepare the sandwiches.
Grease the bottom of a 9x13" baking dish with 1 tablespoon of butter. Using a serrated knife, cut the crusts off the bread slices. In a medium bowl, mix together the chopped giardiniera and olives. Lay 8 slices of bread in the baking dish, spread each slice with 1 teaspoon of the Giardinera mixture, top with 1 slice of salami, 1 slice capicola, 1 slice of ham, 1/2 slice of provolone and another slice of the bread with 1 teaspoon of Giardinera mixture. Repeat layering with remaining meat and bread. In the end, there will be 5 layers of bread and 4 layers of sandwich fixings.