Begin by placing the shallots, garlic and thyme in a container, along with the Marsala, port and brandy. Cover and marinate in the fridge overnight.
Remove the marinated mixture from the fridge and place in a saucepan. Gently and slowly heat the mixture until nearly all the liquid has evaporated to form a glaze, stirring regularly to prevent the shallots and garlic from catching. Remove the pan from the heat, discard the thyme and allow the mixture to cool.
Preheat the oven to 100°c / 212°f. In the meantime, fill a deep roasting tray two-thirds full with water. Ensure that it is large and deep enough to hold a terrine dish or loaf pan. Place the tray in the oven. Place the terrine dish in the oven to warm through while the parfait is prepared.
Preheat a water bath to 50°c / 122°f.
To prepare the parfait, combine the livers with salt in a sous vide bag.
Put the alcohol reduction, along with the egg, in a second sous-vide bag, and the butter in a third bag.
Seal all 3 bags under full pressure and place them in the preheated water bath for 20 minutes.
Carefully remove the bags from the water bath, and place the livers and the egg-alcohol reduction in a deep dish.
Using a hand blender, blitz the mixture well, then slowly incorporate the melted butter. Blend until smooth. It is important to remember that all three elements should be at the same temperature when combined, to avoid splitting the mixture. Pass the mixture through a fine-mesh sieve.
Carefully remove the terrine from the oven, pour in the smooth parfait mixture and place the terrine in the bain-marie. Check that the water level is the same height as the top of the parfait. Cover the bain-marie with aluminium foil.
After 35 minutes, check the temperature of the centre of the parfait using a probe thermometer. The parfait will be perfectly cooked when the centre reaches 64°c / 147°f. This can take up to an hour.
Remove the terrine from the oven and allow to cool to room temperature. Cover with clingfilm and place in the fridge for 24 hours.
Remove the terrine from the fridge and take off the clingfilm.
The top layer of the parfait may have oxidized to grey, so scrape the discoloured part off the surface and you're left with pink. Spoon the parfait into a spherical silicone mould.
Using a palette knife, scrape the surface of the moulds flat, then cover with clingfilm. Gently press the clingfilm on to the surface of the parfait and place the moulds in the freezer until frozen solid.
Taking one tray at a time from the freezer, remove the clingfilm and lightly blowtorch the flat side of the parfait, being careful to only melt the surface. Join the two halves together by folding one half of the silicone mould on to the other half and press gently, ensuring the hemispheres are lined up properly.
Remove the folded half of the mould to reveal a joined-up parfait sphere, and push a cocktail skewer down into it.
Place the moulds back in the freezer for 2 hours (the spheres are easier to handle once frozen solid). Remove them from the mould completely, and smooth any obvious lines with a paring knife.
Wrap the perfectly smooth spheres individually in clingfilm and store in the freezer.
They should be placed in the freezer for at least 2 hours before dipping in the mandarin jelly.