Place the smoked haddock, bay leaf, and peppercorns in a pan and cover with the milk. Place on the heat and bring to a gentle simmer for 4 minutes, then turn off the heat and set aside.
For the Vegetables
Prepare the asparagus by trimming off the bottom couple of centimetres and cut in half.
Bring a pan of salted water to the boil and add the asparagus, sugar snaps, and peas for one minute. Strain and refresh in ice-cold water, then drain and set aside.
Heat the butter in a large heavy-bottomed frying pan over medium-high heat and add the asparagus, sugar snaps, and peas and heat for three to four minutes to cook through. Remove from the heat and season.
For the Poached Eggs
Heat a medium-sized pan of water to a gentle simmer and add the white wine vinegar. Gently stir the water to create a gentle whirlpool and crack in one egg. Cook for three to four minutes, depending on the size then carefully remove with a spoon and place on kitchen paper. Cook the remaining eggs.
For the Beurre Blanc
Place the wine, vinegar, shallots, and herbs in a small pan and bring to the boil. Reduce by half until the liquid is syrupy.
Reduce the heat to the lowest possible setting and add the butter piece by piece, whisking continuously. When all of the butter has been added, remove from the heat, correct the seasoning and strain the sauce using a sieve.
Spoon the vegetables onto four plates. Remove the smoked haddock from warm milk with a fish slice and place it on the vegetables. Top each piece with a poached egg and drizzle with the finished sauce.