Cut the eggplant into slices, about 5mm thick. Place them in a colander, and sprinkle with the 3 tablespoons of salt. Leave for 30 minutes to release the bitter juices and rinse under cold water. Pat dry with kitchen paper.
Preheat the oven to 220C/425F degrees.
Place the sliced eggplant, zucchini, onions, peppers and garlic in a roasting tin (will probably require two tins for this).
Drizzle the olive oil over the vegetable. Season with the thyme, salt and pepper.
Roast in the oven for 30-35 minutes, turning half-way through cooking, until golden brown and tender. When the vegetables are cooked, reduce the oven temperature to 180C/350F degrees.
In a small bowl, beat the eggs and yogurt. Season with the salt and pepper.
Put half the roasted vegetable slices in a layer in a large ovenproof dish. Spoon the tinned chopped tomatoes over and season with the oregano, salt and pepper. Repeat the layers.
Pour the yoghurt mixture over the vegetable layers and crumble the Feta cheese on top. Bake in the oven for 35-40 minutes until golden brown.