Preheat the oven to 450 degrees F (230 degrees C).
Line a baking sheet with parchment paper or silicone baking mats.
Combine eggplant, olive oil, salt and black pepper in a large skillet over medium-high heat. Cook and stir until eggplant begins to soften, about 5 minutes.
Mix in minced onion and red pepper flakes. Reduce heat to medium; cook and stir until onion softens, 4 minutes.
Stir in chicken broth and marinara sauce. Reduce heat to medium-low and simmer until sauce mixture has reduced by half, about 30 minutes.
Whisk bread crumbs, egg, and Greek yogurt in a large bowl until the bread crumbs absorb all the liquid, about 3 minutes.
Mix onions, garlic, Kosher salt, black pepper, cumin, cinnamon, and coriander into the bread crumb mixture.
Crumble lamb into bread crumb spice mixture; stir in cayenne pepper.
Form lamb mixture into small meatballs and transfer to prepared baking sheet. Place baking sheet into the preheated oven and bake until browned, but still pink inside, about 10 minutes.
Remove meatballs from the oven and stir into simmering sauce. Simmer over low heat until sauce begins to thicken, 30 to 45 minutes.
