4 tablespoons unsalted butter, softened, plus more for the pan
1 (10- to 12-ounce) day-old or stale baguette, sliced 1/2 inches thick
3 tablespoons Dijon mustard
6 ounces French-style or thin-sliced deli ham
1 ½ cups whole milk
1 ½ cups half-and-half or heavy cream
4 large eggs
2 egg yolks
Freshly ground black pepper
3 ounces Gruyère cheese, shredded (about 1 cup)
1 ounce finely grated Parmesan cheese (packed 1/4 cup)
Parsley, leaves torn, mustard, and cornichons, for serving (optional)
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.
Trans Fat: 0 grams
Fat: 24 grams
Calories: 400
Saturated Fat: 13 grams
Unsaturated Fat: 9 grams
Sodium: 761 milligrams
Sugar: 6 grams
Fiber: 2 grams
Carbohydrate: 26 grams
Protein: 20 grams