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Quarter the cauliflower so you can easily cut out the thick central stem. Chop the remaining cauliflower roughly.
Melt the butter for the soup in a large saucepan. When it bubbles, add the onion and soften over a gentle heat for a few mins, stirring regularly. When it looks translucent, add the cauliflower, cover the pan and cook for a further 5-6 mins, shaking the pan once or twice.
Add the milk, raise the heat slightly and simmer, partially covered, for 20 mins until the cauliflower is soft enough to purée easily. Let stand for 5-10 mins, then liquidise in batches in a blender or food processor. You can make ahead to this point: leave to cool and refrigerate for up to a day or freeze for up to a month.
To make the garnish, boil the eggs for 8-9 mins, drain and leave to cool. Cube the bread and process to crumbs. Melt a knob of butter in a large frying pan, add the crumbs and fry over a medium heat until golden brown. Keep moving the crumbs to colour them evenly, adding the second knob of butter if the bread soaks up the first. Tip the crisped crumbs onto kitchen paper, shake over a pinch of salt.
Shell and halve the eggs. Separate yolks from whites and push through a sieve or chop both very finely.
To serve, add the cream or extra milk to the soup, reheat and check the seasoning. Mix crumbs, egg yolks and whites with the chopped parsley. Ladle the soup into six warm bowls and sprinkle about 1 tbsp of the garnish in the middle of each, leaving a nice clean band around the edges. Pass the remaining garnish round at the table.
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