Make enough brine to generously cover the eggs.
Allow to soak for 12 days.
Rinse thoroughly under running, room-temperature water until the water runs clear.
Dry the eggs, place them in an airtight plastic bag, and store inside an opaque container.
Age for 4 weeks at 68–77ºF/20–25ºC.
To make the pickled ginger
Put the water, vinegar, and sugar in a saucepan and bring to a boil.
Meanwhile, slice the ginger thinly and place in a bowl.
Pour the boiling liquid over the ginger.
Allow to cool to room temperature, then vacuum pack.
Store in a refrigerator for at least 3 days.
To make the potage
Melt the butter in a pan and sweat the bacon, cabbage, and onion.
Season with salt and cayenne pepper.
Cover with the chicken stock and cream.
Bring to a boil, cover with a lid, and simmer until tender (about 45 minutes).
Remove the bacon and discard.
Purée the mixture left in the pan and pass through a chinois.
To make the ginger cream
Put the cream and water in a pan and bring to a simmer.
Transferto a blender, add the salt, sugar, and xanthan gum, and blend on a low setting for 4 minutes to hydrate the gum.
Add the ginger juice and Versawhip.
Transfer into an ISI canister and charge with 2 cream chargers.
When you’re ready to serve, cook the eggs in boiling water for 1 minute.
Shock in iced water, then peel.
Cut the eggs in half and season with salt and the juice from the pickled ginger.
Chop a little bit of the pickled ginger and put a small amount in the center of each bowl.
Place a dollop of the whipped ginger cream on top of the ginger and place the quail eggs on top.
Serve the potage piping hot.