To make the slow-cooked eggs, preheat oven to 350°F.
Double wrap your cardboard container of eggs in foil.
Bake for 1 hour, then reduce heat to 225°F and bake at least 4 hours or overnight.
Sprinkle kosher salt over the eggplant. Drain in colander for at least 1 hour.
To make the squash and eggplant (you can do this a day in advance), preheat oven to 400°F.
Cut up squash and place slices on a baking sheet. Coat with oil and dust with salt and sugar.
Grease baking sheet with oil, then place eggplant slices in a single layer, making sure not to overlap. Sprinkle with garlic powder, then drizzle with a little more oil.
Bake the squash and eggplant for 15-20 minutes until golden.
Combine the first six ingredients for the salad in a serving bowl. Dress with lemon, olive oil, salt and pepper 10-15 minutes before serving.
