To make the smoked eel brandade, put the milk in a pan and bring to the boil, then remove the pan from the heat and add the smoked eel. Leave the eel to marinate in the warm milk for 10 minutes, then strain the eel and discard the milk. Steam the white fish until it flakes.
Put the eel and fish in a small bowl. Using a fork, mash them together with 30 g (1 oz) of softened butter. Drizzle over 20 ml (¾ fl oz) of olive oil and all of the lemon juice, mixing with the fork as you go. Add the mashed potato and mix well. Add the remaining butter and olive oil and mix well. Season to taste with sea salt. Allow the mixture to cool, then fold in the crème fraîche. Place the mixture in the refrigerator for at least 1 hour.
Take some of the mixture in the palm of your hand and roll into balls the size of a small marble. You will need 16 balls. You may have some mixture left over, which you can use elsewhere.
To make the eggwhite pearls, put the grapeseed oil in a small saucepan and heat to 70°C (165°F). Using an eye-dropper, drop the strained eggwhite into the oil, drop by drop, in rapid succession. When you have about 30 eggwhite droplets, stop and gently stir them around. They need about 1 minute in the oil to fully set. Carefully strain out the eggwhite pearls using a fine sieve and place the pearls on a flat metal tray. Repeat this process several times until you have a sufficient amount of eggwhite pearls to coat the balls of brandade.
To cover the brandade mixture with the eggwhite pearls, first line 16 demitasse cups with 12 cm (4 ½ inch) squares of plastic wrap. Put 1 teaspoon of eggwhite pearls in the middle of the square and spread them out so they form a single layer. Place a ball of brandade in the centre. Carefully lift up the four corners of the plastic wrap and twist them together to form a ball, then tie a knot in the plastic. The aim is to coat the brandade ball in the eggwhite pearls with the aid of the plastic wrap. When you have 16 perfectly covered balls, put them in the refrigerator until required.
Peel the radishes and cut into 3 cm (1¼ inch) thick slices. Using a 2 cm (¾ inch) round pastry cutter, cut out cylinders from the radish. Use a mandolin to slice the cylinders into 1 mm (1/32 inch) thin discs. You will need 96 discs (six discs per flower, for a total of 16 flowers). Blanch the radish discs in boiling water for 10 seconds and refresh in iced water. Dry the discs thoroughly.
Lay 15 cm (6 inch) squares of plastic wrap over 16 demitasse cups, leaving a slight dip in the middle of the plastic. Place six overlapping discs of radish in the centre of the plastic wrap to form a small circle. Place an eggwhite and smoked eel pearl in the centre and pull each corner of the plastic wrap together so the slices of radish come up the sides of the pearl. With your fingers, pinch the base so the radish petals stick to the pearl. Refrigerate in the demitasse cups for 1 hour.