Prepare the leek: trim off the root end and discard the very dark top. Set aside the white part, and keep about a 6 cm section of the green part.
Place the duck giblets (excluding the liver), garlic clove and the green leek section into a pot with about 1 litre of cold water.
Bring slowly to the boil. As it heats, skim off any foam that rises to the surface using a slotted spoon.
Thinly slice the white part of the leek (or onion) and chop the carrots and broccoli.
Add the sliced leek, carrots, broccoli and stock cubes to the pot.
Reduce the heat and simmer gently for 20–25 minutes, until the vegetables are tender.
Add the green peas and chopped kale (or other greens) and cook for 5 minutes more.
Add the leftover roast duck meat for a couple of minutes to warm through.
Finely chop the duck liver and add it to the soup. Bring back just to the boil, then immediately turn off the heat and cover. The residual heat will cook the liver without making it tough.
Serve hot with a splash of apple cider vinegar and a scattering of chopped parsley.