Mix the butter and sugar together with a flat beater to obtain a smooth, even mixture. Add the eggs one by one and the flour. Finally, add the lime zest. cover in clingfilm and set aside. Grease rectangular tins 10 cm x 4 cm (2 cm deep) and cook for 6 min at 160°C (320°F).
Beat the eggs with the sugar until the mixture turns pale. Heat the lemon juice, cook the mixture as you would a crème pâtissière, bringing to the boil and cooking for 3 min. Add the gelatine, previously softened in cold water. Leave to cool and add the fresh butter.
Blanch the lemons 4 times. Leave to cool and chop finely. Bring the orange juice, vanilla, lemon and lime and the first quantity of the sugar to the boil. Add the second quantity of sugar, previously mixed pectin. Boil for 2 min, pour into a dish, cover in clingfilm and set aside.
Heat the lime pulp, the sugar and the kaffir lime zest. Soften the gelatine in cold water and put it in the mix. Leave to cool and add the whipped cream, mix gently, and transfer into transparent plastic tube-shaped containers with diameters of 3.5 cm. Leave to cool.
Mix the sugar, water, milk and leave to cool. Add the lemon and lime juice, the zest, the star anise and infuse 10 min. Strain and leave to cool. Process and set aside in the freezer.
Blanch the zest 3 times. Prepare a syrup using the water and sugar. Add the zest and leave to simmer on a low heat. Set aside.
Make a syrup from the water and the sugar and allow the star anise to infuse. Add the supremes and leave to steep overnight.
Temper the white chocolate. Make a white chocolate lattice half-cylinder and set aside.
Fill the pastry case with lemon marmalade to 0.5 cm deep and then add the lemon cream to 1.5 cm. Position the lemon and kaffir lime roll, cover it with the half-cylinder of white chocolate. Decorate the plate with the zest and candied supremes. Use the lemon, lime and star anise sorbet to make a quenelle.