Cook the omelettes according to one of the master recipes, but leave them slightly underdone. Slip each as it is made onto a buttered plate, then slide it onto the buttered platter, arranging the omelettes side by side.
Cut a slit along the length of each omelette to within ½ inch of the 2 ends. Fill the slits with the tomato purée.
(*) If not to be used immediately, rub tops of omelettes with softened butter and cover with waxed paper.
Preheat broiler to very hot.
Just before serving, pour the cream over the omelettes, and sprinkle with cheese and melted butter. Set platter 3 inches from hot broiler for 1 or 2 minutes to reheat the omelettes and to brown the cheese lightly, but do not let the omelettes overcook. Serve immediately.