In a heavy-bottom saucepan, combine the water and 1 cup sugar. Cook over high heat until the sugar has fully dissolved.
Stir in the cranberries and orange liqueur. Reduce the heat to medium and cook for about 10 minutes, stirring occasionally, until the berries burst and the mixture thickens slightly.
In a small bowl, whisk together the egg yolks, cornstarch, and salt until smooth. Slowly drizzle in a small amount of the hot cranberry mixture while whisking constantly. This prevents the yolks from scrambling.
Pour the tempered yolk mixture back into the saucepan with the cranberries. Simmer for about 5 minutes, stirring often, until the filling thickens and coats the back of a spoon. It should look glossy and feel a bit like warm jam.
Remove from heat, then stir in the vanilla extract and butter until completely smooth.
Pour the filling into your prepared, baked pie crust and let it sit at room temperature for 30 minutes, then transfer it to the refrigerator to chill. This step is key. The cranberry filling continues to thicken as it cools, giving you those perfect clean slices later.
In a clean mixing bowl, whisk the egg whites (not yolks) and cream of tartar until foamy.
Gradually add the remaining sugar, beating continuously until stiff, glossy peaks form. Spread the meringue evenly over the cooled filling, making sure it touches the crust to seal.
Broil for 1–2 minutes, watching closely, until the meringue is lightly golden.