Heat a skillet over medium heat and add the olive oil.
Add the onion and ground turkey and cook until the turkey is browned, about 10 minutes.
Add the tomato sauce, herbs and spices and simmer for an additional 20 minutes.
Heat a saucepan over medium heat and add butter; stir to melt. Add the flour and cook for 2 minutes. Whisk in the milk and simmer until thick.
Crack the eggs into a bowl and temper them by whisking in a small amount of the milk and flour mixture. Add that to the saucepot and continue whisking while bringing to a boil. Remove from the heat and stir in 1/4 cup of the cheese. Season with salt and pepper.
Arrange half of the eggplant on the bottom of a 10-inch cast-iron skillet. Spread the turkey over the top and then top with the rest of the eggplant slices.
Pour the custard over the top and sprinkle the rest of the cheese on. Cover and bake 45 minutes, then uncover and cook an additional 10 minutes.