Beat the eggs with cream; season with salt, pepper and a little nutmeg. Add the Parm and combine.
Combine the honey, mustard, thyme and lemon juice in a small bowl. Spread on one side of the bread slices. Build the sandwiches of prosciutto and cheese. Turn the sandwiches in the egg mixture.
Melt a few tablespoons of butter in a large pan over medium heat. When the butter foams, cook until the sandwiches are golden and the cheese has melted. Cut them corner to corner and serve with an orange and scallion or red onion salad dressed with EVOO, salt and pepper alongside.