Preheat the oven. Heat your oven to 375°F (190°C). Line a rimmed baking sheet with parchment.
Make the béchamel. Melt 3 Tbsp unsalted butter in a saucepan over medium heat. Once melted, whisk in 3 Tbsp flour then continue to cook for 1-2 minutes, until the flour is a light golden brown. Slowly pour in 2 cups of milk, whisking the entire time. Continue cooking until the sauce is rich, thick, and creamy, about 3 minutes. Season with ½ tsp kosher salt, ¼ tsp black pepper, and a pinch of ground nutmeg. The béchamel should be spoonable, not thick or gluey.
Toast the bread. Lightly toast all bread in a toaster oven (or regular oven). No need to add butter.
Assemble the sandwiches. Working on a cutting board, spread soft butter on the outside of each slice, then flip over. Next, spread a thin layer of whole grain mustard on the inside of two slices, followed by a thin layer of béchamel. Top each with a light layer of shredded Gruyère, a folded slice or two of Parisian ham (don’t fold flat), and then a bit more Gruyère. Spread a little béchamel on the inside of the remaining two slices, then fold over onto the assembled sandwiches. Spread another thin layer of béchamel on top, finish with a generous sprinkle of Gruyère, then transfer to the prepared baking sheet.
Bake first. Bake the sandwiches for 10-12 minutes, or until the cheese has heated through and begun melting.
Broil to melt the top. Set the broiler to high. Carefully move the oven rack as close as it’ll go towards the heating unit. Broil the sandwiches for 1-2 minutes, until golden brown and bubbling. Keep a close eye on them so they don’t burn.
To make a Croque Madame: While the sandwiches are broiling, make two fried eggs (either sunny-side-up or over easy, based on your preference), then slide one on top of each sandwich just before serving. The yolk should be just runny enough to act like a sauce. Top with thinly sliced chives or chopped fresh parsley.
To serve: Either way, because this sandwich is so rich, the preferred way to enjoy it is with a light, refreshing salad on the side. Enjoy!