6 ounces unsalted butter, divided
2 tablespoons flour
1 cup whole milk
1 bay leaf
1/2 teaspoon kosher salt, plus more for seasoning
1/4 cup grated Parmesan
8 slices thick sourdough bread
8 to 12 slices good quality ham (about 3/4 pound)
12 ounces Gruyere cheese, grated, divided
Nonstick spray
4 eggs