For the halibut, heat a frying pan until hot, add the butter and heat until it turns a nut-brown colour. When the beurre noisette reaches 50C, lower the halibut into the butter and poach for 5 minutes.
Preheat the barbecue. Oil a double layer of kitchen foil and put the potatoes in the centre of the foil with the lavender and the garlic. Season with salt and pepper and seal the potatoes in a parcel by crimping the long edges together and folding the edges in to create a solid seal. Cook on the barbecue for 30-40 minutes.
Blanch the samphire in boiling water for 30 seconds. Drain and stir through a knob of butter.
Melt a knob of butter in a large saucepan. Add the shallot and carrot and cook for 1–2 minutes. Add the mushrooms and cook for a further 2 minutes.
Add the champagne and reduce by half. Add the stock and bubble away until the volume has reduced by half. Add the cream and reduce again. Stir through the caviar and check the seasoning
Serve the halibut with the samphire and the barbecued new potatoes with the champagne caviar sauce poured over.