Oil a shallow square metal or silicone baking tray, about 18 x 18cm. Put the sugar in a pan with the cream of tartar and 500ml water and heat gently at first, stirring so that the sugar melts. Then, turn up the heat and boil for 10-15 mins until the mixture is a little more syrupy. If you have a sugar thermometer, it should reach 115-118C.
Stir the cornflour into 150ml water, then, whisking all the time, pour it into the sugar syrup. Keep whisking, until everything combines to make a smooth, gloopy mix. Take out the whisk and start to stir with a spatula or spoon over a medium heat. Keep stirring until the mixture is thick enough to see a clear line drawn through it with the spoon and it starts to leave the sides of the pan. It will be very thick and make big bubbles that burst as it cooks, so be careful. This can take up to an hour. Test the mix by dropping a small amount into very cold water; it should form a ball that can be pressed gently when cold and that will feel a little springy.
Stir in the rosewater or rose syrup and the food colouring, if using, then pour everything into the tray and level the top. Leave to cool and set completely. Sieve some cornflour and icing sugar together over a board and carefully turn out the Turkish delight. Cover it with more icing sugar and cornflour and cut it into cubes with a sharp knife. Dust with yet more of the icing sugar mixture and move the pieces apart so they can dry. Can be stored openly or in small cardboard boxes or bags.