In a wide bottom pan over medium heat, sauté the onion and garlic in the olive oil until soft and golden. Add the ground lamb, turn the heat to high and cook until brown and cooked through. Stir in the thyme, oregano, and cinnamon. Add the white wine and tomatoes. Simmer over medium heat for 15 minutes to reduce to a sauce consistency and to combine flavors. Season with salt and pepper.
Trim that tops off the eggplant. Cut lengthwise into ½ “ thick slices. Lay on a sheet pan and salt on both sides. Allow to sit for 20 minutes. Press on the slices with a dry kitchen towel to absorb the liquid the eggplant releases. Turn over and repeat on the other side. Heat a large skillet over high heat. Add a couple tablespoons of olive oil and cook as many slices of eggplant as will fit in the pan. Brown on one side and turn to cook on the other. Remove to a sheet pan lined with paper towels to absorb any excess oil.
In a small saucepan over low heat, melt the butter and stir in the flour to combine. Cook for two minutes and remove from the heat. In a separate saucepan, heat the milk with the bay leaf to a simmer. Whisk in the butter, flour mixture. Bring back to a low simmer stirring constantly to avoid lumps. Season with salt and the ground nutmeg.
Preheat oven to 375°F. To assemble the moussaka, lay a third of the eggplant slices in a 14”x 10”casserole dish so that they cover the bottom and are slightly overlapping. Spoon half of the meat sauce over top of the eggplant slices. Smooth the sauce with the back of a spoon or spatula and repeat with another layer of eggplant. Spoon the remaining meat sauce into the dish. Smooth and repeat with the remaining slices of eggplant. Spoon the white sauce on top. Smooth with the back of a spoon or spatula. Scatter the cheese over the top and bake for 45 minutes until cheese is brown. Remove from the oven and allow to cool slightly before serving.