Preheat your oven to 450℉. Bring a large pot of salted water to a boil for the pasta.
Grease a large baking sheet. Toss the eggplant with 4 tbs oil and a large pinch of salt. Spread on the baking sheet and roast until crisp and brown, 15 to 20 minutes.
In a large skillet over medium-high heat, heat the remaining tbs oil. Add the ground lamb. Cook, breaking up with a wooden spoon, until crumbled and cooked through. No pink traces should remain. Now add 2 of the minced garlic cloves and the shallot. Cook one minute more, until softened and cooked. Add salt, Aleppo pepper, and black pepper. Stir in the mint or dill and cook another minute to let the flavors marry together. Add the eggplant and keep on very low heat until ready to assemble the dish.
Cook the past in the boiling water according to package directions. Meanwhile, in a small, preferably stainless steel saucepan, melt the butter. Cook until it turns golden brown and smells nutty. Yep, you’re browning butter!
In a small bowl, combine the yogurt and remaining garlic clove with a pinch of salt. Stir until smooth.
Now, to assemble. Drain the pasta and spread it out onto a large platter. Top with the lamb-eggplant mixture. Dollop the yogurt sauce, then pour the melted brown butter evenly over the entire platter. Sprinkle on more Aleppo pepper and extra mint or dill. Serve immediately.