Boil 500ml water with brine ingredients, remove from heat, and cool.
Spatchcock the quail with scissors, cover with cooled brine, and chill for 30 minutes.
Remove quail, pat dry, and season with oil, salt, and pepper.
Cook quail on a hot griddle pan for 3.5 minutes per side until skin is browned.
Mix onion, chestnuts, cranberries, and parsley together for the salad.
Whisk dressing ingredients, soften squash in them for 5 minutes, then combine with salad.
Sauté the finely chopped garnish chestnuts in oil for 1-2 minutes.
Plate the quail, drizzle with chestnuts, and serve with the salad.