In a large pan over medium heat, warm a splash of olive oil until shimmering.

Add the finely diced onion and sauté for about 4 minutes until softened and translucent.

Stir in the peeled and cooked chestnuts, cooking for an additional 2 minutes until well combined.

Pour in water and add the fresh rosemary. Bring to a gentle boil.

Add the bouillon cube and let the soup simmer for about 15 minutes.

Use a hand blender to carefully blend the mixture until smooth and creamy, about 1-2 minutes.

Return the soup to low heat and stir in the milk, heating for another 5 minutes.

Taste and adjust seasoning with salt and pepper as needed.

In a separate pan, melt butter and sauté the extra chestnuts until crispy, about 3-4 minutes.