Bring the honey to a boil with chili flakes and ½ tsp smoked paprika powder.
Remove from the heat and leave to stand for two minutes.
Stir in 1 tbsp apple cider vinegar and allow to cool completely.
Carefully separate the four egg yolks, keeping them fully intact. (keep 1 egg white for the Parmesan crisps).
Pour the cooled honey into a deep dish and gently slide in the yolks, making sure they are completely submerged.
Refrigerate for 24 hours.
Carrots (1 day ahead)
Peel the carrots and place them on an oven rack.
Cook for 2 hours at 130°C until tender. Then dry them for 3 hours in the oven or dehydrator at 60–70°C.
Cool the carrots in the refrigerator.
Cold-smoke them with oak chips for 5–10 minutes.
Vacuum-seal the smoked carrots with a little olive oil and freeze.
Defrost again in time for serving.
Pickled shallot
Peel the shallot and slice into very thin rings.
Bring the apple vinegar, sugar and bay leaf to a boil, dissolving the sugar.
Remove from the heat, add the shallot rings and allow to cool at room temperature.
Parmesan crisps
Preheat the oven to 170℃.
Grate the the Parmesan with a very fine microplaner.
Mix the egg white, parmesan, flour, water and salt with a hand mixer.
Fill the mold with the mixture as cleanly as you can. Put it in the oven for 8 to 10 minutes. If you're making them for the first time, make sure to keep an eye on them once they're in the oven for 5 minutes. Not every mold might be the same and not every oven is as exact about the temp. You want them perfectly golden.
Take the mold out as soon as the crisps are perfectly golden. Put it down for 30 seconds and then carefully remove the shapes from the mold and put them on a sheet of baking paper.
Seaweed mayonnaise
Finely chop the seaweed salad and mix it with the mayonnaise.
Tartare
Dice the carrots into very small cubes.
Make a dressing using some olive oil, a little of the pickling liquid from the shallots, a little of the honey used for the egg yolks, salt and pepper. Mix well and fold through the diced carrot.
Plating
Place a red chicory leaf on each plate. Position a cooking ring at the wide end of the leaf, fill with the carrot tartare and press down gently so it holds its shape when the ring is removed.
Top each tartare with some pickled shallot rings and one honey-cured egg yolk (let a touch of honey cling to the spoon — it adds a beautiful accent).
Pipe small dots of seaweed mayonnaise onto each tartare and finish with cress and the Parmesan crisp.