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Melt the butter in a frying pan over a medium heat until foaming, then fry the leeks with a pinch of salt for 5-10 mins until soft. Leave to cool slightly.
Put 200g soft breadcrumbs, the thyme, egg yolks, cheese, mustard and a generous grinding of pepper in a bowl and mix to combine. Stir in the fried leeks, and any butter left in the pan. Season with salt and mix well using your hands.
Mould the mixture into 12 sausages (divide and weigh for accuracy if you like). You may find damp hands help, cleaning your hands every so often to stop them sticking. Transfer to a baking tray lined with baking parchment and freeze for 10 mins until firm, or chill for 30 mins in the fridge.
While the sausages are firming up, whisk the egg whites in a shallow bowl with a pinch of salt until lightly foamy. Put the flour and some of the remaining breadcrumbs onto separate plates.
Dust the chilled and firm sausages in the flour, then dunk in the egg white, and roll in the breadcrumbs. Top up the plate of breadcrumbs as required. Chill for at least 1 hr and up to 24hrs before frying.
Heat the oven to 180C/160C fan/gas 4. Heat the oil in a non-stick frying pan over a medium high heat. Fry the sausages in batches, turning them gently every minute, for 4-6 mins, until golden and crisp all over. Add a little more oil between batches if you need to. Transfer to a baking tray, and bake for 10 mins. If you are freezing the sausages, once they're golden brown transfer to a tray and leave to cool for a few minutes, then open-freeze (uncovered) until solid and transfer to freezer-proof containers. Will keep frozen for up to three months. Cook from frozen in the oven for 25 mins until piping hot.