Peel and finely slice the onions. Scrub and dice the carrot (no need to peel unless you want to). Top and tail the courgettes and chop them into 1cm pieces. Trim any thick, woody stems from the kale and shred the leaves.
Peel and crush the garlic cloves. Peel and finely grate the ginger. Finely grate the lemon zest. Separate the coriander leaves from their stalks (pop the leaves aside for later in the recipe), and finely chop the stalks.
Pour 1 tbsp olive oil into a pan and bring to a medium heat. Slide in the chopped onions, carrot, courgettes, garlic and ginger. Stir in 1 tsp turmeric, 1 tbsp mild curry powder, the lemon zest, chopped coriander stalks and a good pinch of salt and pepper. Cook for 5-6 mins, till the vegetables have slightly softened.
Stir in the shredded kale, followed by the rice. Pour in 300ml boiling water. Return to the boil, then cover the pan and reduce to a simmer. Cook for 15 mins, till the rice is tender.
While the vedgeree cooks, fill a small pan with water and bring to the boil. When the water is hot, carefully add the whole eggs. Simmer for 7 mins (8 for firmer yolks). Lift the eggs out and plunge into a bowl of cold water. Let them cool for a couple of mins.
Stir half the crème fraîche through the rice and squeeze in the juice from half the lemon. Taste and add more lemon juice, salt or pepper if you think it needs it.
Drain the eggs and peel away the shells. Slice in half. Pile the vedgeree onto warm plates and top with the eggs, the reserved coriander leaves and dollops of the remaining crème fraîche.