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To make the chilli oil, tip the shallots, garlic, cinnamon stick, star anise and oil into a wide pan (a deep frying pan is good), then bring to a gentle sizzle. Cook for 15-20 mins over a low-medium heat, stirring now and again, until the shallots and garlic are crisp and golden brown. They will burn easily if the heat is too high, so watch the pan.
Meanwhile, toast the sesame seeds in a dry pan until golden, then tip into a bowl and set aside. Put the cumin seeds and Szechuan peppercorns in the pan and toast for 1-2 mins until aromatic. Tip into a pestle and mortar or spice grinder, and grind to a powder. Mix with the toasted sesame seeds.
Add the ginger, chilli flakes, soy and sugar to the bowl with the toasted, ground spices. When the shallots and garlic are crisp, strain the oil over the bowl using a sieve. Leave the crispy bits of garlic and shallot in the sieve to cool and become even more crisp. Discard the cinnamon and star anise.
Stir the cooled shallots and garlic through the spiced oil mixture. Will keep chilled for up to two weeks in an airtight, sterilised jar.
When ready to make the noodles, heat the veg oil in a wok. Add the pak choi and stir-fry for a minute with a splash of water and a pinch of salt. Cover with a lid (or a baking tray if you don’t have one). Steam for a minute, then lift the veg from the wok, letting any liquid drip off. Set aside on a plate. Put the vinegar, soy sauce, sesame oil and sugar in the pan along with 2 tsp of the crispy chilli oil. Bring to a bubble, then add the noodles and toss for a few minutes over a high heat until the sauce is clinging to the noodles and they’re soft and slippery. Divide the noodles between two bowls and put the pak choi on top.
Wipe out the pan. Add another drizzle of the crispy chilli oil along with about 2 tsp of sediment from the jar. When sizzling, crack in the eggs and fry until crispy around the edge, spooning over the oil as they cook. Slide the fried eggs over the noodles, adding more crispy bits from the jar, if you like.