Preheat the oven to 180C/350F/Gas 4.
Sprinkle some salt onto a baking tray and place the butternut squash on top. Roast in the oven for 30 minutes, or until soft. Once cool enough to handle, chop the squash into fine dice, discarding the seeds. Reserve one quarter of the chopped squash for garnish.
Heat a saucepan until hot, add the olive oil then the roasted squash, carrot, shallot, garlic, thyme, bay leaf and sage and fry for 4-5 minutes. Cover with the stock, bring to a simmer and cook for 10 minutes, or until the vegetables have softened.
Season with salt and freshly ground black pepper. Blend in a food processer until smooth and pass the mixture through a fine sieve into a clean saucepan.
Poach the egg yolks in a pan of simmering water at 65C-70C/150F-160F. Remove with a slotted spoon and set aside to drain on kitchen paper.
For the persillade, mix the herbs, garlic and shallots together until well combined.
To serve, place the egg yolks in flat soup bowls. Shave the cheddar with a potato peeler. Place the cheese over the yolk and sprinkle with the persillade. Place the reserved squash around the egg yolk then pour the soup around the edge and serve.