Generously butter a 9-inch by 13-inch baking pan.
Butter the slices of bread on one side and spread a thin layer of mustard on the other side.
Arrange, shingled, over the bottom of the pan, buttered side up; not to worry if all the bread is not used.
Drape evenly with ham.
In a medium bowl, whisk together milk, half-and-half, egg, egg yolks and pepper.
Pour evenly over the bread and ham.
Sprinkle with Gruyère and Parmesan cheeses, allowing the ham to peek out in places.
Cover and refrigerate for 30 minutes (for the bread to sop up the milk) or up to overnight.
When ready to bake, pre-heat oven to 325°F and
Place in the pre-heated oven and bake until the custard is set and the bread and cheese are golden brown; 40 to 45 minutes.
Remove from the oven and allow to set 20 minutes before scattering evenly with parsley.
Scoop and serve warm or at room temperature with parsley, mustard and/or cornichons.
