To make the dressing: Place the mustard, honey, white wine vinegar and a little salt and in a bowl. Whisk in the olive oil, lemon juice and chives. Taste for seasoning. Set aside.
To poach the Hake: Pour approximately 200ml water into a shallow frying pan which is big enough to fit the hake fillets in a layer. You will need enough to cover the fish. Add in the lemon slices, sprigs of parsley, black peppercorns and a little salt. Bring to the boil. Reduce the heat and gently slide in the hake fillets. Simmer for 10 minutes.
Meanwhile in a separate saucepan heat some water, add the sliced carrots and salt and pepper. Cook for 2-3 minutes. Add the leeks and continue to cook for another couple of minutes until the vegetables are tender. Drain well.