To make the purée, melt a small knob of butter in a saucepan, add the celeriac and cook over a medium-high heat until starting to brown a little, about 5 mins. Pour over the milk and cream, and season well – the celeriac should be just covered, so add more milk if needed. Bring to a simmer, cover and cook for 15 mins or until tender. Drain, reserving the cooking liquid, and transfer to a food processor. Blend until smooth, then sieve into a clean saucepan, pushing the celeriac through with the back of a spoon or spatula. Add a little of the cooking liquid to loosen the purée if needed, and taste for seasoning.
To make the crumbs, heat a small knob of butter in a frying pan, add the breadcrumbs and cook, stirring, until golden brown. Throw in the capers and cook for 30 secs more. Tip into a bowl and leave to cool a little, then stir through the parsley.
Heat oven to 140C/120C fan/gas 2. Gently melt the butter in a small ovenproof saucepan or frying pan, big enough for the fish fillets to fit snugly. Once melted, add the shallot, bay leaf and peppercorns. Keep heating until the butter turns a light brown colour and smells nutty. Leave to cool a little. Gently lower the fish fillets into the warm butter, basting any exposed fish, and transfer to the oven. Cook for 3-4 mins, depending on the thickness of the fish, then turn the fillets over and cook for a further 3-4 mins or until just opaque and feeling firm.
While the fish cooks, reheat the purée and steam the greens. To serve, spoon the purée into the centre of each plate; use the back of the spoon to spread out slightly into a circle. Top with the greens, then carefully place the halibut on top. Drizzle with a little of the poaching butter and scatter with the crumbs.