Beat eggs with cream; season with salt, pepper and a little nutmeg. Add Parm and combine.
Combine honey, mustard, thyme, lemon juice in a small bowl. Spread on one side of the bread slices. Build sandwiches of prosciutto and cheese. Turn sandwiches in the egg mixture.
Melt a few tablespoons of butter in a large pan over medium heat. When butter foams, cook until 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.