Peel, rinse and slice potatoes. Grease baking pan with 3 tablespoons of oil and spread potatoes in it, season with salt and pepper and cover with aluminum foil. Parboil for 20 minutes in preheated oven at 200°C (approximately 400°F).
Rinse and dry eggplants, trim the ends and slice into 1 cm (approximately 1/2 inch) thick slices. Season with salt generously and let stand for 15 mintues. Rinse in cold water and pat dry. Blanch tomatoes in hot water, rinse in cold water and peel, slice. Rinse and dry zucchini, trim the ends and slice.
Peel onions and garlic. Dice onions, heat 4 tablespoons of oil in a pan and saute onions for a few minutes. Remove from the pan and saute meat, in portions if necessary, until crumbly. Season with salt, pepper and thyme, add squeezed garlic and onions and tomato pieces from the package. Heat oil in another pan and brown eggplant slices, few at a time. Drain on paper towels. Brown zucchini slices in the same pan on both sides. Spread meat mixture over potatoes. Arrange eggplant, zucchini and tomato slices on top, alternating. Season with salt and pepper.
Whisk eggs with milk and pour over moussaka. Bake for about 40 minutes in the oven or until golden. Garnish with sage leaves and serve.