Peel, wash, halve and slice the parsley roots. Peel shallots and cut into cubes. Melt the fat in a pot at medium heat, fry the shallots and parsley roots in it. Add white wine and stock. Simmer covered for 30-40 minutes.
Take out 1/3 of the parsley roots and put aside. In the meantime, wash the parsley and pluck the leaves. Blanch the parsley in boiling salted water for about 2 minutes, then rinse. Put parsley and 2 tablespoons of oil in a universal chopper and mix. Season to taste with salt and pepper and place in a small bowl. Add cream and milk to the soup and season with salt, pepper and sugar. Mix finely with a hand blender and add parsley root slices. Cut black pudding into slices. Heat 2 tablespoons of oil in a pan and fry the black pudding until golden brown. Pour the soup into bowls and spread the black pudding slices on top.
Add cream and milk to the soup and season with salt, pepper and sugar. Mix finely with a hand blender and add parsley root slices. Cut black pudding into slices. Heat 2 tablespoons of oil in a pan and fry the black pudding until golden brown. Pour the soup into bowls and spread the black pudding slices on top. Drizzle with some parsley oil. Pass the rest of the oil extra