To bake the potatoes
Preheat the oven to 200°C/400°F/gas mark 6. Wash the potatoes in cold water and then brush with a little oil and dust with sea salt to draw the moisture out of the skin. Bake the potatoes for 1-1¼ hours or until tender. Remove from the oven and set aside to cool slightly; when cool enough to handle, cut in half, scoop out the flesh, retaining the skin, and pass the flesh through a fine sieve into a saucepan, add the butter and mix through to incorporate thoroughly. Set aside and keep them warm.
To make the sauce
Heat the cream, mustard, lemon zest and juice together in a pan until it comes to the boil. Take it off the heat, whisk in the egg yolks until combined, then stir in the Parmesan and add the basil. Season to taste with sugar, salt and freshly ground black pepper and continue to cook until the sauce thickens. Serve the sauce warm when needed.