Line a 9-inch bowl with plastic wrap, press the softened ice cream into it and freeze for at least 4 hours until solid.
Trim the cake into a 9-inch circle, invert the frozen ice cream dome onto it and remove the plastic wrap.
Freeze the assembled cake and ice cream for 1 hour while heating the oven to 500°F.
Beat the egg whites, cream of tartar and salt to soft peaks, add the sugar gradually and beat to stiff glossy peaks; beat in the vanilla.
Cover the ice cream and cake completely with a thick continuous layer of meringue and bake for 3 to 5 minutes until browned, then slice immediately.