Put the milk, lemon zest and garlic into a saucepan. Bring to the boil over a medium heat. Remove from the heat, add the fish and set aside for 15 minutes, or until the fish is cooked.
Meanwhile, cook the potatoes and celeriac in a pan of salted boiling water, for 5-10 minutes, or until tender. Drain.
Mash the potato and celeriac, then beat in the butter, olive oil and enough of the poaching liquor to make a smooth mash.
Remove the fish from the pan. Chop half of the fish and beat it into the potato mixture; flake the remaining fish.
Spoon the brandade into a bowl, top with the flakes of cod and sprinkle over the parsley.