First prepare the chips. Rinse the potatoes in water to remove the starch. Immerse them in boiling water for 6 minutes, then drain and dry them on kitchen paper. Now double-fry them in the sunflower oil: first at 140ºC for 4 minutes (leaving to cool afterwards), then at 180ºC until crisp and golden. Season with salt.
Preheat the grill so that it is hot. Cut the lobsters in half and season with salt; pour over the clarified butter and place the lobsters on a grill tray. Cook under the grill for 8–10 minutes until cooked through; the internal temperature should have reached 68ºC. You may need to do this in batches; if so, keep the cooked lobsters warm on a plate under foil.
For the sauce, heat the stock, let it boil, then whisk in the cold butter until emulsified. Finish with salt, the lemon juice and tarragon. Scoop out the cooked head meat and anything left on the grill tray and put it into the sauce.
Serve the lobsters and chips with a green salad. Drizzle the sauce over the salad and lobsters.