For the Chicken Liver Parfait:
Place the shallots, garlic, and thyme in a saucepan with the Madeira, Port, and brandy. Marinate for 24 hours. Heat the marinated mixture until nearly all the liquid has reduced, stirring regularly to prevent shallots and garlic from burning. Remove from heat and discard the thyme.
Preheat the oven to 100°C. Fill a bain-marie with 5 centimeters of water and place in the oven. Preheat a water bath to 50°C. Sprinkle salt over the livers and put them in a vacuum seal bag. Put the eggs, reduced mixture, and livers in a heated blender and incorporate at 50°C until smooth. Slowly blitz in the butter and blend until smooth. Pass through a fine sieve, pushing with the back of a small ladle.
Pour into a terrine dish and place in the bain-marie, covering with aluminum foil. Cook until the parfait’s center reaches 64°C. Remove from the oven and cool. Refrigerate for 24 hours before serving.
For the Mandarin Jelly:
Gently heat the purée and glucose in a pan to combine. Add the gelatin and stir until dissolved. Remove from heat and add oil and paprika extract, and stir well. Pass through a fine sieve and reserve until required.
To Assemble and Serve:
Using a spoon, fill dome molds with the parfait, ensuring there is enough pressure to create a completely smooth surface. Level off the tops so they are flat and cover directly with plastic wrap. Place in freezer until completely frozen.
Gently de-mold the domes and place on a board flat side up. Very briefly run a blow torch over the parfaits’ flat side so the surface begins to melt. Join the two halves together and compress, wrapping well in plastic wrap. Insert a popsicle stick into the round part of each parfait ball. Place back in freezer.
Gently melt the mandarin jelly in a saucepan and cool to room temperature. Remove the plastic wrap, dip each parfait ball into the jelly, and stand the sticks upright, using plastic wrap to hold them up. Refrigerate for 1 minute and then repeat the dipping process twice more. Place the balls onto a tray covered in plastic wrap, and defrost in the refrigerator for at least 6 hours.
Once defrosted, gently mold the ball using your thumb into the shape of a mandarin. Place a stalk and leaf at the top to complete the fruit.