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Heat oven to 325 degrees and generously butter a 9-by-13-inch (or 1 1/2- to 2-quart) 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; you may not need all the bread. Drape evenly with ham.
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. 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 mustard and cornichons.