Bring a large pot of salted water to a boil. Blanch eggplant slices in the boiling water for 1 minute. Rinse slices under cold water, then drain on paper towels.
Blanch tomatoes in the boiling water for 1 minute. Rinse in cold water, then remove skins. Cut tomatoes into quarters and remove and discard the cores. Chop tomatoes coarsely.
Heat olive oil in a saucepan over medium heat. Add onions and garlic and sauté until translucent, about 5 minutes. Add lentils and tomato paste; sauté briefly. Add vegetable broth, cover, and bring to a boil. Reduce heat to low and simmer for 15 minutes.
Add chopped tomatoes, zucchini, savory, cinnamon, and cumin. Cover, increase heat, and bring to a boil. Reduce heat to low and simmer for 10 more minutes.
Preheat the oven to 425 degrees F (220 degrees C).
Pour 1/2 of the lentil mixture into the bottom of a large oven-proof dish. Cover with 1/2 of the eggplant slices. Pour remaining lentil mixture over top and cover with remaining eggplant slices.
Mash feta cheese with a fork; mix with yogurt and eggs. Season with salt and pepper. Spread over the eggplant layer.
Bake in the center of the preheated oven until golden brown, about 25 minutes.