Trim and cut the carrot into small cubes. Peel and finely chop the onion. Heat a pan. When warm, drizzle in 1 tbsp olive oil. Add the carrots and onion. Sweat on a low heat for 5 mins.
Thinly slice half of the mushrooms. Finely chop the rest. Scatter the caraway seeds into the veg and toast for 1 min. Add in the mushrooms and cook for 5 mins.
Tip in the pearl barley and pour in the hot stock. Throw in the bay leaf. Pop on a lid and cook gently for 15 mins.
Peel the potato. Chop it into 1 cm cubes. Finely chop the parsley stalks, reserving the fronds for later. Add the potato and parsley stalks to the pan. Cook for 5-6 mins till the potato is just tender.
Zest and juice the lemon. Add half the zest and juice to the pan. Add most of the dill fronds. Season and taste. Add more lemon juice if necessary. Serve in warm bowls with the remaining lemon zest and parsley leaves on top.