Heat your oven to 200°C/Fan 180°C/Gas 6. Pop the rice in a bowl and cover with cold water. Whisk (you can use a fork) for 1-2 mins till the water is cloudy (this is the starch). Drain, rinse and tip back into the bowl. Cover with cold water and set aside.
Halve the aubergines lengthways. Score a crisscross pattern into the flesh. Put in a roasting tin so they sit snugly. Brush each half with 1 tsp olive oil and season with salt and pepper. Bake for 20 mins till soft.
Peel and finely chop the onion. Peel and grate or crush the garlic. Pick the leaves off the parsley. Finely chop the leaves and stalks, keeping them separate. Warm a deep frying pan or wok for 1 min. Add 2 tsp olive oil and the onion. Season. Stir and fry for 8-10 mins till soft and golden. Add the garlic and chopped parsley stalks. Stir and fry for 1 min.
Stir in the chopped tomatoes. Add 1 tsp each of the cinnamon and sugar. Cover. Bring to a simmer. Turn the heat down and simmer for 10 mins till the sauce has thickened slightly. Stir every so often.
Take the aubergines out of the oven. Scoop out the flesh with a teaspoon, leaving a wall about ½ cm thick around the edge of each aubergine. Roughly chop the scooped aubergine flesh.
Add the chopped aubergine to the tomato sauce. Taste. Add more salt, pepper or sugar if it needs it. Spoon into the aubergine shells. Return them to the oven and bake for 20 more mins till just browned.
While the aubergines bake, drain the rice. Tip it into a small pan. Add 400 ml boiling water and a pinch of salt. Cover. Bring to the boil. Turn the heat down and simmer for 8 mins till all the water is absorbed. Take off the heat and set aside, lid on, for 5 mins to steam.
Arrange the aubergines (your Imam Bayildi) on 2 warm plates with the rice. Scatter over the chopped parsley leaves to serve.