Soak the chicken livers in the milk, 500ml/18fl oz water and two teaspoons of the salt in a shallow dish for one hour. This will draw out most of the blood, which can make the livers bitter, giving the parfait a more delicate flavour. Rinse and drain the livers well.
Preheat the oven to 130C/270F/Gas ½.
Put the Madeira, port, shallots, thyme, garlic and Cognac in a small saucepan and bring to a boil. Let the mixture bubble until reduced by one-third and then remove the pan from the heat. The bitterness of the alcohol will have evaporated off and the flavours of the herbs will infuse into the liquid.
Place the drained chicken livers and the contents of the pan in a blender or food processor and process, adding one egg at a time, for 3-4 minutes, or until the texture is silky smooth.
Gradually add the melted butter (if you add it too quickly, the parfait may split), the remaining salt and the pepper. Taste the mixture and correct the seasoning if necessary.
Line the base and sides of a 23cm x 9cm x 8cm/9in x 3½in x 3in terrine tin with greaseproof paper, leaving a 3cm/1in overlap above the top of the tin. The paper will protect the parfait from direct heat and prevent it discolouring and becoming hard.
Using the back of a ladle, press the parfait mixture through a fine sieve into a large bowl then pour into the terrine tin and cover with another piece of greaseproof paper cut to fit.
Place the terrine in a deep baking tray and pour in boiling water until it reaches two-thirds of the way up the sides of the tin. This bain marie method of cooking allows the heat of the oven to permeate through the water and cook the parfait very gently so that it is cooked though evenly.
Cover the tray loosely with a sheet of perforated foil and place it in the oven. Check the temperature of the parfait with a temperature probe after 40 minutes – the parfait is cooked when the middle has reached 65C-70C/150F-158F. Do not overcook or it will split and lose its fine texture.
When the parfait is cooked, remove the terrine tin from the baking tray, leave it to cool for 30 minutes at room temperature then refrigerate.
Discard the greaseproof paper from the top of the parfait then dip the tin in a deep tray of hot water. Slide a hot knife between the sides of the tin and the greaseproof lining then hold the edges of the lining and carefully lift the parfait from the tin onto a chopping board.
Peel away the greaseproof paper from the sides of the parfait. Warm a palette knife in hot water and smooth the top and sides of the parfait, trimming away any discolouration on the top. Return the parfait to the fridge for at least 30 minutes to firm it up, or place it in the freezer for 15 minutes.
To finish, beat the softened butter and lard together and spread a thin layer over the top of the parfait using a palette knife.
Line a flat baking tray with a sheet of clean greaseproof paper. Flip the parfait over onto the tray and spread the remaining butter/lard mixture over the sides and what has now become the top. Covering all the surfaces of the parfait with this mixture will prevent it from oxidising and discolouring.
Return the parfait to the fridge and chill for at least one day before serving; two days is ideal.
To serve, dip a knife into hot water and cut the parfait into thick slices. Serve with chutneys, pickles and toasted sourdough bread, or spread onto crostini to serve as canapés. Red Burgundy is the perfect wine match.