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1
Place the split peas, mirepoix vegetables, bouquet garni, and ham hock in a large pot. Cover with 1.5 L of light stock. Bring to the boil, skim thoroughly, then reduce to a steady simmer. Cook for 45–60 minutes (20 minutes for fresh peas). The peas are done when they collapse completely under light pressure between thumb and forefinger.
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2
Remove the ham hock and bouquet garni. Pass the soup in batches through a blender or food mill, then push it through a fine chinois (conical sieve) with a ladle, pressing firmly. This is where the dish lives or dies: the chinois removes all fibre and creates the velvet texture that defines a potage — a blended but unsieved preparation is a purée, not a potage. The soup emerging from the sieve should be perfectly smooth and uniform in colour.
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3
Return the sieved soup to a clean pot. Adjust the consistency with additional warm stock or a small addition of cream — the potage must flow freely and evenly from a ladle; if it holds a mound, it is too thick.
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4
Over a low heat, finish the soup by whisking in the 30 g of cold butter a few cubes at a time (monter au beurre), followed by the small pour of cream. The surface should carry a visible sheen. Taste and correct the seasoning. The soup must be served very hot; bring it back to temperature if necessary, taking care not to boil once the butter is incorporated.
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5
Fry the 1 cm bread cubes in clarified butter, turning frequently, until golden and crisp on all sides. Drain on paper. Add the croutons to each bowl only at the moment of service — if they are added earlier they go soggy.
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6
Ladle the soup into warmed bowls. Place a small cluster of fresh pea shoots and a few chervil pluches at the centre, then scatter the croutons around them. Serve immediately.