To make the stock, combine the ham hocks and chicken stock or water in a large pot. Bring to a simmer over low heat and skim off any scum or impurities. Add the vegetables, herbs, and spices and cook uncovered for about 4 hours, until the hocks are very tender.
Remove from the heat and allow the meat to cool in the stock.
Once the meat and liquid have cooled, carefully remove the hocks from the stock and shred the meat into bite-sized pieces, discarding the skin and cartilage. Reserve the meat and pass the stock through a fine sieve to remove the solids.
Heat the oil in a large saucepan over medium heat. Gently cook the onion and leek, stirring occasionally, until soft but not coloured. Add the peas and mint. Combine the milk, cream, and 1 litre/4 ó cups of the ham stock in another saucepan and bring to a rapid boil. Pour this hot liquid over the vegetables and cook until the peas are tender. The trick here is to cook the soup quickly, which preserves the color of the peas.
Cool the soup rapidly to retain the beautiful 'spring' color, then process it in batches in a food processor until smooth. Season to taste with salt and pepper. Return to the pan and reheat to warm (50-60°C).
To make the mint crème fraîche, whisk the creams together until firm peaks form. Mix in the mint, and season to taste.
To serve, divide the soup between serving bowls and add the ham hock meat.
Garnish with a tablespoon of the mint crème fraiche.