Whisk the milk the sugar together in a small saucepan and bring to the boil over a low heat. Meanwhile, combine the lime juice, egg yolks and cornflour in a mixing bowl; whisk till smooth.
Just after reaching the boil, remove the milk-sugar mixture from the heat and gradually whisk it into the lime mixture. Pass through a fine sieve back into the saucepan. Cook over low heat, whisking constantly, until it thickens. Scrape into a small bowl, press clingfilm directly against the surface and chill thoroughly (this can be prepared up to 3 days ahead).
For the lime curd
Melt the butter in a medium saucepan. Off the heat, whisk in the egg yolks, sugar, lime juice and lime zest.
Set the pan over a medium heat and whisk until the curd gets hot and steam starts to emerge. Decrease the heat to low and continue whisking until the curd thickens. Take care not to let the curd come to the boil; move the pan on and off the heat as needed.
Strain into a stainless steel bowl or clean plastic container; press clingfilm directly against the surface and chill until cold.
Pipe the chilled lime curd in a spiral on the base of the baked tart case. Cover with the chilled lime cream, filling the case to the top; use a metal spatula to spread the top smooth and flat. Cover and freeze the tart solid.
For the meringue
Combine egg whites and sugar in a heatproof mixing bowl and set it over a pan of boiling water; whisk until all the sugar has dissolved. Whisk on medium-high speed until the egg whites have risen in volume but are still creamy and not dry.
Top the frozen tart with the meringue. Bake in a preheated 190 C / Gas 5 oven for 7 to 8 minutes until the meringue is golden. Remove from oven and keep the tart at room temperature until fully defrosted.
Unmould and slide the tart onto a serving plate. Use a thin, sharp knife to cut it and wipe with a wet cloth between cuts.
The lime curd makes more than you will need, but it will last for weeks if tightly covered and refrigerated.