Preheat your oven to 200°C/ 392 ℉. Place the potatoes on little mounds of rock salt on a baking tray and bake for 50 minutes–1 hour, until cooked.
Remove and leave for a few minutes until cool enough to handle, then cut the potatoes in half, scoop the flesh out into a bowl, and mash until smooth. Leave to cool.
Once the mashed potato is cool, add the crabmeat, spring onions, dill, capers, gherkins, and a little salt and pepper. Mix together well then taste to check the seasoning and correct as necessary.
Divide the crab mixture into 4 equal portions and roll into balls in your hands. Have the flour, beaten eggs, and breadcrumbs ready in 3 separate bowls.
Pass each crab cake through the flour, then the egg mixture, and, finally, the breadcrumbs to coat evenly. Place in the fridge until ready to cook.
To make the lemon sauce, put the shallots, garlic, lemongrass, and wine in a pan and cook until the wine has almost totally reduced.
Add the cream and turn the heat down low.
Now add the butter, piece by piece, whisking all the time; do not allow the sauce to boil or it will split. Once all the butter is incorporated, season with salt and pepper to taste. Strain the sauce through a sieve into a bowl and cover the surface with cling film or baking parchment to prevent a skin forming. Keep warm.
Heat the oil in a deep-fryer or other suitable deep, heavy-based pan to 170 °C/ 338 ℉. Lower the crab cakes into the hot oil and fry for 3–4 minutes until golden and cooked through.
Meanwhile, gently warm the sauce and add the sliced basil.
Share the sauce between 4 warmed plates or shallow bowls. Carefully lift the crab cakes from the pan, drain on kitchen paper and season with salt. Place a crab cake on each pool of sauce and finish with a drizzle of olive oil. Serve immediately.