Slice eggplant lengthwise into ½-inch thick pieces and lay them flat without overlapping. Sprinkle with salt and let sit for 15 minutes, then pat dry with paper towels.
Preheat the oven to 400°F and spray a 9×13" baking dish with olive oil.
Heat 1 tablespoon of olive oil in a skillet and grill the eggplant slices in batches for a few minutes per side, seasoning as you go.
In the same skillet, heat 1 tablespoon olive oil and sauté the shallot for 1-2 minutes. Add garlic and cook for 30 seconds.
Stir in ground meat and cook until no longer pink, breaking it apart with a wooden spoon. Season with chili powder, dried oregano, paprika, salt, and pepper.
Pour marinara sauce into the skillet, stir to combine, and adjust seasonings if needed.
In a small bowl, mix breadcrumbs and pecorino cheese. Sprinkle a few tablespoons of the mixture on the bottom of the baking dish.
Layer eggplant slices on the bottom, add half the sauce, spread evenly, and sprinkle with one-third of the cheese.
Repeat with another layer of eggplant, the remaining sauce, and more cheese. Top with a final layer of eggplant, the rest of the cheese, and the breadcrumb-pecorino mixture.
Add 1 ½ cups of mozzarella cheese and ⅓ cup of Parmesan cheese to the ricotta mixture, stirring well.
Spread ½ cup of the prepared meat sauce in the bottom of a lasagna pan.
Add 4 slices of eggplant over the sauce, then spread half the ricotta mixture on top of the eggplant.
Layer half the meat sauce over the ricotta mixture, then repeat the layers, topping with the remaining mozzarella and Parmesan cheese.
Repeat with another layer of eggplant, the remaining sauce, and more cheese. Top with a final layer of eggplant, the rest of the cheese, and the breadcrumb-pecorino mixture.
Cover the dish with foil and bake for 35 minutes.
Uncover and bake for 5-10 more minutes until golden brown.
Let cool slightly before slicing.