Moussaka on the Grill

Name: Moussaka on the Grill
Ingredients: 1 1/2 pounds eggplant, peeled and cut crosswise into 1/4-inch-thick slices; Kosher salt and freshly cracked black pepper; Extra-virgin olive oil, for drizzling; 1 pound ground beef (or 8 ounces ground beef and 8 ounces ground lamb); 1 large yellow or red onion, peeled and diced; 5 cloves garlic, sliced; 2 tablespoons tomato paste; 1 cup red wine; 2 fresh bay leaves; 1 cinnamon stick; Small bunch fresh oregano; One 28-ounce can crushed tomatoes; 6 tablespoons unsalted butter; 1/2 cup all-purpose flour; 2 1/2 cups whole milk; 1 teaspoon freshly grated nutmeg; 1 cup grated pecorino; 2 large egg yolks; Zest of 1 lemon; Pecorino, for serving; Fresh flat-leaf parsley, for garnish