Croque Madame

Name: Croque Madame
Ingredients: 3 Tbsp. unsalted butter; 3 Tbsp. all-purpose flour; 2 cups whole milk; 3½ cups (12 oz.) coarsely grated Gruyère cheese, divided; ½ cup finely grated Parmesan cheese; Kosher salt and freshly ground black pepper; Freshly grated nutmeg; Twelve ¾-in. slices pain de mie or other white Pullman bread, toasted; ¼ cup plus 2 Tbsp. Dijon mustard; 12 thin slices baked ham; 2 Tbsp. canola oil; 6 large eggs