Place a medium-size pot over medium heat and melt 2 tablespoons butter. Sprinkle the flour over the melted butter and cook for about 1 minute. Slowly whisk the milk and mustard into the butter-flour mixture. Season it with some fresh nutmeg, salt and freshly ground black pepper, and cook for about until it thickens up.
Place four slices of bread on the counter. Spread some of the sauce onto each slice of bread, then lay down some ham, a couple slices of cheese, another smear of sauce and top each sandwich with the remaining bread slices.
Place a large skillet over medium-high heat and melt the remaining tablespoon of butter. In a high-sided dish, whisk up the eggs. Dip the sandwiches in the egg and transfer them to the hot pan. Cook until golden brown, 3-4 minutes per side.
While the sandwiches are cooking, whisk the raspberry jam, white vinegar, EVOO, some salt and freshly ground black pepper in a large salad bowl. Toss the salad greens in the dressing and serve them up alongside the best ham and cheese you've ever had!