Roll out dough on a floured work surface to a 12-inch round. Transfer to a standard 9-inch pie dish. Trim to a 1-inch overhang, then fold overhang under itself until flush with edge of plate. Crimp edge as desired or simply flatten slightly to an even thickness for an undecorated crust.

Refrigerate until firm, about 30 minutes (or freeze for 10 minutes). Preheat oven to 375˚F.

Line pie crust with parchment and fill with pie weights. Bake until bottom of crust is set and dry, about 30 minutes. Remove parchment and weights. Continue baking until golden, 10 to 12 minutes more. Let cool completely on a wire rack.

In a small saucepan, bring cranberries, ¼ cup sugar, and pomegranate juice to a boil, stirring until sugar dissolves. Boil until cranberries burst and mixture thickens to a loose jam, 7 to 9 minutes. Strain through a fine mesh sieve into a large bowl, pressing on solids to extract liquid and pulp.

In a small bowl, stir together gelatin and 2 tablespoons cold water. In another saucepan, whisk together egg yolks, milk, salt, and ¼ cup sugar to combine. Cook over medium heat, stirring frequently, until mixture thickens slightly (a thin batter consistency), 5 to 7 minutes. Remove from heat.

Stir gelatin into egg yolk mixture, then stir into cranberry mixture to combine. Cover surface with plastic wrap (to prevent a skin from forming), and refrigerate until mixture is cool and begins to set along edges, about 30 minutes.

In a bowl, beat egg whites and remaining ⅓ cup sugar to stiff peaks (do not overmix). Stir ⅓ of the meringue into the chilled cranberry mixture to lighten, then gently fold in remaining meringue just until no streaks remain and filling is a uniform color.

Transfer to baked crust, smoothing the top with an offset spatula. Refrigerate until filling is cold and set, at least 4 hours or loosely covered up to 2 days. Top with whipped cream and sparkling cranberries to serve.