Preheat the oven to 450F. Toss the sliced eggplant in one tbsp olive oil. Lay the eggplant on a baking sheet and bake for 20 minutes or until brown. Set aside.

Place a medium pot over medium heat. Add 2 tbsp of oil and once hot, add the onions and cook for 3 minutes. Add the garlic and cook for another minute. Add the ground lamb. Break the meat up with a spoon and cook until brown. If you see a lot of rendered fat, remove some of the fat before proceeding.

Add the mint, oregano, cinnamon stick, bay leaf, and 2 tsp of salt and 1/2 tsp black pepper. Cook for another 3 minutes. Add the tomato paste and cook for 5 minutes. Add red wine and scrape off any of the bits that have formed on the bottom of the pan.

Add the canned tomatoes and bring it to a boil over high heat. Once it comes to a boil, bring the heat down to medium and let it simmer for 30 minutes. Remove the cinnamon stick and bay leaf. Taste for salt and pepper.

Meanwhile, place two large russet potatoes in a pot of cold water. Bring to a boil and cook until the potatoes are easily pierced through with a knife. Drain and set aside to cool. Once it's cool enough to handle, slice the potatoes into 1/4" thick rounds.

To make the béchamel, heat the butter over medium heat in a saucepan. Once melted, add the flour and stir to combine. Whisk constantly for one minute. Whisk in the milk and Let it come to a simmer. Keep whisking to prevent the bottom from burning. Once it thickens, remove it from the heat Season with 1/2 tsp salt and stir in half of the cheese.

Once it has cooled down a bit, stir in the egg yolks. Mix to combine.

In a 9x13 pan, add the lamb and spread the mixture into an even layer. Layer on the eggplant and then the potatoes. Top it off with the béchamel and spread into an even layer. Top with the rest of the cheese and bake for about 30 minutes until the top is golden brown and bubbling. Let it cool a bit before serving.