Make the orange syrup: Combine the orange juice, sugar and water in a small skillet over medium heat. Bring to a simmer and cook until syrupy and reduced by half, 3 to 5 minutes. Let cool.
Meanwhile, make the ice cream cakes: Coat four 6-ounce freezer-proof bowls or ramekins with cooking spray and line with plastic wrap, leaving a 2-inch overhang. Divide the sherbet among the ramekins; use a piece of plastic wrap to press the sherbet into the center and up the sides to create a cup shape. Fill the centers with small scoops of vanilla ice cream and spread evenly. Arrange the ladyfingers on top in a single layer, breaking to fit, then drizzle with the orange syrup. Cover with the overhanging plastic wrap and freeze until very firm, at least 4 hours or overnight.
Make the meringue: Beat the egg whites and cream of tartar in a large bowl with a mixer on medium-high speed until foamy, 30 seconds to 1 minute. Gradually beat in the sugar, then increase the mixer speed to high and beat until stiff shiny peaks form, 4 to 5 minutes. Add the vanilla and beat until combined. Transfer to a large piping bag fitted with a 3/8-inch round tip.
Uncover the ice cream cakes and invert onto a foil-lined baking sheet. Let stand until the ice cream cakes slip out of the bowls easily, then remove the plastic wrap. Pipe the meringue around each ice cream cake in a spiral. Freeze until firm, at least 3 hours or up to 2 days.
Brown the meringue with a kitchen torch (or bake at 500˚ until golden, 3 to 5 minutes). Use a spatula to transfer the baked Alaskas to a platter or plates.