Slice your eggplant 1/2 inch thick lengthwise. Lay the slices on a flat surface with no over lapping. Sprinkle with salt and wait 15 minutes. Pat and wipe dry with paper towels.
Preheat your oven to 400°F. Spray a 9x13" baking dish with olive oil.
In a large skillet, working in 3 batches, heat 1 tbs olive oil per batch and grill the slices, a few minutes per side. Season each side of the eggplants as you go.
IN the same skillet, heat 1 tbs olive oil and saute your shallot for 1-2 minutes and then stir in the garlic for 30 seconds. Add in the ground meat and use a wooden spoon to break apart the meat until no longer pink. Season with chili powder, dried oregano, paprika, salt and pepper to taste. Pour in the sauce and mix to combine. Taste and adjust any seasonings if needed.
Mix your breadcrumbs and pecorino in a small bowl. Sprinkle the bottom of the baking dish with a few tablespoons. Set down one layer of eggplant slices. Add on them HALF the sauce and spread out evenly. Sprinkle with one third of the cheese. Repeat again with the eggplant slices, then the rest of the sauce, and some cheese on that. Top layer is one more eggplant and then final is the cheese. Top with the remaining of the breadcrumb-pecorino mixture. Bake COVERED for 35 minutes. Uncover and bake for another 5-10 minutes or until top is golden brown. Allow to cool slightly prior to slicing.