Sauté the Onions: In a large pan, heat a tablespoon of olive oil over medium heat. Add the chopped onion with a pinch of salt and sauté for about 4 minutes until soft.

Add the Chestnuts: Stir in the peeled and cooked chestnuts and cook alongside the onions for an additional 2 minutes.

Introduce Liquid and Herbs: Pour in enough water to cover the chestnuts and add the fresh rosemary. Bring to a gentle boil.

Simmer the Soup: Once boiling, add a vegetable bouillon cube, stirring to dissolve. Lower the heat and simmer uncovered for 15 minutes.

Blend Until Smooth: Take off heat and use a hand blender to puree the mixture until smooth.

Stir in Milk: Return the blended soup to low heat and gradually stir in the milk. Warm through gently for another 5 minutes.

Season to Taste: Taste and season with salt and freshly ground black pepper.

Sauté Whole Chestnuts: In a separate frying pan, melt a tablespoon of butter over low heat. Add whole chestnuts with a pinch of salt and sauté until golden brown.

Serve and Garnish: Ladle the soup into bowls and top with sautéed chestnuts and a sprig of fresh rosemary.