Take the loin out of the fridge an hour before it is needed so it can reach room temperature. Preheat the oven to 80°C (176°F).
Mix the soy sauce, mirin, sake, sugar, ginger and garlic in a saucepan and bring to the boil. Lower the heat and simmer for 10-15 minutes until it thickens. Strain to remove the garlic and ginger and allow to cool.
Sear and brown the loin on a medium-high heat in some neutral oil on all sides. Use a brush to glaze the loin with the teriyaki sauce and place in the oven. Cook for about 40-60 minutes to a core temperature of about 54°C (129°F), basting it with teriyaki sauce every 10 minutes so it gets a nice thick glazing.
Cook the Udon noodles according to the instructions on the pack. Stir-fry the vegetables and add some sauce, then season with pepper and salt.
Slice the loin and serve with the noodles and vegetables, sprinkled with some finely sliced spring onions and sesame seeds.
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