In a large cooking pot, add pumpkin, season with salt and cook for 10 minutes (stirring constantly).Add vegan buttermilk, vegetable broth and garlic (peeled and chopped). Lower the heat and cook for 10 minutes.
Blend the soup using a blender. Set aside.
Rinse, dry and finely chop parsley. Heat a little olive oil in saucepan, add chestnuts and cook for 5 minutes. Transfer to a dish.
Divide the chestnuts among bowls, sprinkle with chopped parsley. Pour the soup over them.