Peel and finely dice shallot. Peel the parsnips and cut into 2 cm pieces. Peel and grate the ginger.
Heat the butter in a large saucepan. Sauté shallots in it over medium heat for 3 minutes until translucent. Add the peas, ginger and parsnips and sauté for another 3 minutes while stirring. Add the bay leaf, white wine and 750 ml stock and bring to the boil, covered. Add milk, cover again and bring to the boil over a mild heat for 30 minutes.
Now divide 100 g of the chestnuts into sixths. Caramelize the sugar in a pan until light brown. Pour in 80 ml of stock (be careful, it splatters!). Stir in chestnuts and cook over a mild heat until the liquid has almost evaporated.
Heat the remaining 200 g chestnuts in the soup for 5 minutes. Puree the soup very finely with the cutting stick (or in the mixer) and add 1 - 2 squirts of lemon juice to taste.
Pour the soup into preheated plates and serve garnished with caramel chestnuts and a little garden cress.