Eggplant Gratin

INGREDIENTS

• 1/4 cup ricotta cheese
• Kosher salt
• 1/4 cup half-and-half
• 3/4 pound eggplant, unpeeled, sliced 1/2-inch thick
• 1/2 cup good bottled marinara sauce
• Good olive oil, for frying
• 1/2 cup plus 2 tablespoons freshly grated Parmesan
• Freshly ground black pepper
• 1 extra-large egg