This takes a classic French sandwich, the Croque Madame, and turns it into a savory breakfast casserole. It’s a pretty smashing dish to look at, will make your kitchen smell incredible (thank you Gruyère!) and is excellent paired with a simple green salad with, what else, a French vinaigrette.
In a large shallow bowl, whisk together the eggs, milk, Dijon, salt, and a generous shower of black pepper.
Tuck a piece of ham between each slice of bread with a bit poking out the top. Divide it up so the ham is evenly distributed among the slices.
Set aside about ¼ cup of the cheese. Tuck the rest of the cheese between the slices of bread. Do the same with the arugula, so there is a bit of greenery between each slice.
Pour the remainder of the egg mixture over the casserole. Scatter the remaining ¼ cup of cheese over the top.
Bake until the outside is nice and crusty with the inside tender and any egg that has spilled to the edges firm, about 35 minutes.