Heat oven to 375°. On a lightly floured surface, roll dough into a 12″ round. Fit into a 9″ pie plate. Trim edges and crimp; chill 30 minutes. Using a fork, prick the dough all over. Line dough with parchment paper and fill with pie weights or dried beans; bake until golden, about 20 minutes. Remove paper and weights and bake until cooked through, about 5 minutes more; let cool.
Bring 1½ cups cranberries, ½ cup sugar, plus cranberry juice and salt to a simmer in a 2-qt. saucepan over medium-high heat. Cook, stirring occasionally, until cranberries burst and soften, 8–10 minutes. Let cool slightly, then transfer to a blender with cranberry liqueur and lemon juice; purée until smooth. Pass through a fine-mesh strainer into a bowl, pressing on and discarding solids; chill.
Combine gelatin and 3 tbsp. ice-cold water in a bowl; let sit to soften gelatin, about 5 minutes. Beat ⅓ cup sugar with egg yolk and milk in a 2-qt. saucepan over medium heat. Cook, stirring, until thick, 8–10 minutes. Remove from heat; stir in gelatin and cranberry mixtures until smooth. Transfer custard to a bowl and place a layer of plastic wrap directly over the surface to prevent a skin from forming; chill until just beginning to set at edges, about 30 minutes.
Whisk egg whites in a bowl until stiff peaks form. Stir ¼ of the whites into chilled custard; using a rubber spatula, gently fold in the remaining whites to combine. Pour filling over dough; using a rubber spatula, spread into an even layer. Chill, uncovered, until set, about 1 hour.
Spread ⅓ cup sugar on a plate. Boil remaining ½ cup sugar with ½ cup water in a 2-qt. saucepan until sugar is dissolved, about 2 minutes. Remove from heat and stir in remaining cranberries. Using a slotted spoon, transfer cranberries to plate; roll in sugar and scatter over top of pie. Whip cream in a bowl until stiff peaks form; using a spoon, dollop cream in center of pie.