Croque-Monsieur Breakfast Casserole

unsalted butter, softened, plus more for the pan

(10- to 12-ounce) day-old or stale baguette, sliced 1/2 inches thick

Dijon mustard

French-style or thin-sliced deli ham

whole milk

half-and-half or heavy cream

large eggs

egg yolks

Freshly ground black pepper

Gruyère cheese, shredded (about 1 cup)

finely grated Parmesan cheese (packed 1/4 cup)

Parsley, leaves torn, mustard, and cornichons, for serving (optional)