Place wild rice in a saucepan with two and half cups of cold water, cover and bring to the boil over a high heat. Turn down and simmer for 25-30 minutes until the water has mostly evaporated. Take off the heat, cover and set aside to finish steam cooking and leave until cool.
Preheat oven to 180°C. Warm the oil in a 25cm oven-proof frying pan or frittata pan on a medium heat. Cook the onions until tender, for 2 minutes, stirring constantly. Add the spring onions and cook a further 2 minutes.
Take off the heat and add the balsamic vinegar and stir. Add the onion mix to the cooled rice mix, add nutmeg and basil, and season to taste with salt and freshly ground black pepper. Mix until well combined.
Remove beetroot from the packaging and cut in half. Return the greased pan to a low heat, spoon in the rice mix. Arrange the beetroot on top of the rice mix, then pour over the beaten eggs, letting it sink into the rice mixture.
Cook dish in oven for 30-35 minutes, until the egg has set. Allow to stand for 10-15 minutes, before serving. Can be served hot or cold.
Rinsing and soaking the rice overnight will help reduce the cooking time. The rice should be soft but slightly chewy.