Preheat the oven to 180C/350F/Gas 4 and cook the quinoa according to packet instructions.
For the filling, toss the eggplant slices in the vegetable oil, then drain and season, to taste, with salt and freshly ground black pepper.
Heat a frying pan over a medium heat, add the eggplant slices in batches and fry for 2-3 minutes on each side, or until golden-brown on both sides. Remove from the pan with a slotted spoon and set aside to drain on kitchen paper.
Add the celery and pepper to the pan and fry for 2-3 minutes, or until softened. Add the tomato purée, stir to coat the vegetables in it, then continue to fry for a further 4-5 minutes.
Add the canned chopped tomatoes and cinnamon stick and simmer for 4-5 minutes. Add the quinoa and return the fried eggplant to the mixture. Simmer for a further 2-3 minutes, or until warmed through. Transfer the mixture to an ovenproof dish and sprinkle over the chopped parsley.
For the topping, in a bowl, beat together the feta, lactose free cream, eggs and grated nutmeg until well combined. Season, to taste, with salt and freshly ground black pepper.
Pour the topping mixture into the ovenproof dish on top of the filling. Sprinkle over the grated parmesan.
Transfer the veggie moussaka to the oven and bake for 25-30 minutes, or until the topping is golden-brown and has set and the filling is bubbling. Serve immediately.