To make the filling, heat 3 tbsp of the oil in a frying pan and gently fry the aubergine slices for 6-8 minutes on each side until golden. You may need to add a little more olive oil at first, but this will be released as the flesh softens. Lift out the aubergine slices and drain on a plate covered with a few layers of kitchen paper.
Add the onion and garlic to the oil remaining in the pan and fry over a gentle heat for 4-5 minutes until soft, adding a little extra oil if necessary.
Chop the spinach finely, by hand or in a food processor. Beat the egg in a large mixing bowl.
Add the spinach, crumbled feta, Parmesan, yogurt, milk and the onion mixture to the eggs. Season well with salt and pepper and stir thoroughly.
Spread the cooked rice in an even layer over the base of the pastry case. Reserve about 8 aubergine slices - save the best ones as these will be placed over the top - and arrange the rest in an even layer over the rice.
Spoon the spinach and feta mixture over the aubergines and place the reserved slices of aubergine on top. Bake at 350 degrees for 30-40 minutes, or until lightly browned. Serve warm or cold, with a mixed salad.