Preheat oven to 400°F (200°C). Line 2 rimmed baking sheets with parchment paper.

In a very large bowl, stir together apple slices, ¼ cup (50 grams) granulated sugar, 1 tablespoon (15 grams) rum, lemon juice, and ¼ teaspoon salt until well combined. Let stand for 15 minutes. Divide apple mixture between prepared pans, spreading into an even layer.

Bake until apples are fork-tender and have released significant moisture, 20 to 26 minutes, rotating pans and stirring mixture halfway through baking. (Apples will be slightly reduced in size but still retain their shape.) Let cool on pans on wire racks. Leave oven on.

Let All-Butter Pie Dough stand at room temperature until slightly softened, 10 to 15 minutes. On a lightly floured surface, roll dough into a 14-inch circle (about ⅛ inch thick). Transfer to a 9-inch deepdish pie plate, pressing into bottom and up sides. Trim dough to ½ inch beyond edge of plate; fold edges under, and crimp, if desired. Freeze until firm, about 20 minutes.

Top dough with parchment paper; add pie weights. Place on a baking sheet.

Bake until edges of crust are lightly golden and just set, 15 to 20 minutes. Carefully remove weights and parchment; bake until inside of crust is dry and just set, 8 to 10 minutes, lightly covering edges of crust with foil to prevent excess browning, if necessary. Let cool completely on pan on a wire rack. Position oven rack in bottom third of oven. Reduce oven temperature to 350 F (180 C).

In another very large bowl, whisk together crème fraîche, egg, flour, vanilla bean paste, remaining ½ cup (100 grams) granulated sugar, remaining 1 tablespoon (15 grams) rum, and remaining   teaspoon (1.5 grams) salt. Fold in cooled apple mixture until thoroughly coated; pour into prepared crust, spreading into an even layer.

Bake until filling edges are just starting to set but mixture is still jiggly, about 25 minutes, lightly covering crust with foil to prevent excess browning, if necessary. Sprinkle Almond Streusel evenly over filling. Bake until streusel is lightly golden, apples are tender, filling is slightly puffed and set, and an instant-read thermometer inserted in center registers at least 162°F (72°C), 35 to 40 minutes more, lightly covering crust with foil to prevent excess browning, if necessary. Let cool completely on a wire rack before slicing, or refrigerate until ready to serve. Garnish with confectioners’ sugar, if desired.