Tip the rice into a small pan. Pour in 450ml boiling water. Add a pinch of salt. Cover and bring to the boil. When the rice is boiling, turn the heat down and simmer for 15-20 mins till all the water is absorbed and the rice is sticky and tender. Stir now and then. Once it’s cooked, take off the heat. Leave in the pan, lid on, to keep warm.
While the rice is cooking, pickle the veg. Pour 2 tbsp cider vinegar into a medium bowl. Add 1 tsp sugar and whisk together with a pinch of salt. Trim and grate the carrot into the bowl. Peel and thinly slice the onion and add to the bowl. Mix and scrunch everything together with your hands. Set to one side.
Peel and grate the ginger and garlic. Halve the chilli and flick out most of the seeds. Finely chop it. Thinly slice the shiitake mushrooms.
Heat a frying pan. When warm, tip in the sesame seeds. Toast for 2-3 mins till golden and nutty smelling. Transfer to a bowl.
Keep the pan on the heat. Add ½ tbsp olive oil and the shiitake mushrooms. Cook for 2 mins then add the ginger, garlic and chilli. Stir for 1 min then add the baby leaf spinach. Cook for 2 mins till wilted. Season lightly. Tip into a bowl and cover with foil to keep warm.
Add the lardons to the pan. You shouldn’t need any oil. Cook, stirring now and then, for 5 mins till golden and crisp. If your pan is big enough, push them to the edge of the pan to make way for the eggs. Or tip them in to a bowl and cover to keep warm.
Add ½ tbsp oil to the pan. Crack in the duck eggs and cook for 2-4 mins, till the white is set and the yolk is as cooked as you like. Turn off the heat.
Pour the remaining vinegar and sugar into the cooked rice and gently stir through. Spoon into deep warm bowls. Top with the shiitake and spinach mix. Scatter over the lardons. Finish with a fried egg each. Sprinkle over the sesame seeds and serve the pickles on the side.