Preheat the oven to 180°C.
Sprinkle salt on a baking tray and roast the squash for 30 minutes until soft.
Dice the squash and reserve one quarter for garnish.
Fry the squash, carrots, shallot, garlic, and herbs in a saucepan for 5 minutes.
Add stock, simmer for 10 minutes, and season with salt and pepper.
Blend the soup until smooth and pass through a fine sieve into a clean pan.
Poach egg yolks in simmering water at 65°C to 70°C, then drain on paper.
Mix the fresh herbs, garlic, and shallots together to create the persillade.
Serve by placing egg yolks in bowls topped with shaved cheddar, persillade, and reserved squash.
Pour the hot soup around the edge of the garnish and serve.