In a large pot on medium heat, melt the butter and add the bacon & onion. Saute for 5-7 minutes, or until the onion is translucent.
Add in the chestnuts and combine well with the onions. Saute until fragrant, about 5 minutes more.
Add in the bone broth, whole milk, half & half, black pepper and salt. Bring to a simmer and cook for 20 minutes, until the chestnuts are tender.
In a blender, puree the soup mixture until velvety smooth. Pour back into the large pot to keep warm. Serve with rosemary, bacon and extra chestnuts for garnish.