Soak the cod in water in the fridge for 48 hours, changing the water four times.
Blanch parsley in boiling water, drain, and blend with 200ml olive oil and salt for two minutes.
Strain the parsley oil through a muslin cloth overnight.
Preheat the oven to 180°C.
Bake the potato on a bed of salt for 1 hour until tender, then peel when cool.
Poach the drained cod in milk with bay leaves, thyme, and garlic until boiling.
Flake the fish to remove bones and skin, then sieve and reserve the poaching milk.
Blend the cod with a portion of potato and a ladle of milk in a food processor.
Drizzle in 600ml of olive oil while blending until smooth and season with white pepper.
Whisk squid ink, lemon juice, and 3 tablespoons of olive oil together in a pan over gentle heat.
Cook seasoned squid on a hot griddle pan for 3-4 minutes.
Top warm brandade with squid, garlic croutons, vinaigrette, parsley oil, and Espelette pepper.