Tip the chicken livers into a colander and rinse gently under cold running water. Drain thoroughly, then pat them dry with paper towel. Using kitchen scissors, trim off any stringy white pieces and any discoloured edges. Season to taste and set aside.
Wipe the mushrooms with a damp cloth to remove any grit but do not wash. Trim the broccolini to remove any coarse or woody stems.
Gently heat the oil in a wok or large, non-stick frying pan. Add the onion and cook, stirring frequently, until it is soft and translucent. Add the livers and gently stir-fry over a medium heat for 2 minutes until they are lightly coloured. Preheat the grill to medium.
Add the mushrooms and broccolini and stir-fry for 2 minutes. Add the garlic, sherry and redcurrant jelly. Stir well, then cover the wok and leave to simmer gently for 3 minutes until the broccolini is just tender when pierced with the tip of a sharp knife and the livers are slightly pink inside.
Meanwhile, toast the ciabatta. Check the stir-fry for seasoning, then arrange the ciabatta on individual plates, two slices per serving, and spoon the livers and vegetables over the top. Serve immediately.