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Step 1
Preheat oven to 325°.
Step 2
For the filling, melt butter in sauté pan over medium heat. Add apples and 2 Tbsp. sugar; sauté until apples are soft but not mushy, 8–10 minutes. Stir in rum and salt. Spread apples over the bottom of the blind-baked crust.
Step 3
Whisk together eggs, egg yolks, cream, 1/2 cup sugar, vanilla, nutmeg, and remaining 1/8 tsp. salt; pour over apples in pie crust. Bake pie until custard is barely set in center, about ⏰ 30 minutes.
Step 4
For the almond topping, combine almonds, sugar, and softened butter, and a pinch of salt in a bowl. Remove pie from oven; sprinkle with topping. Cover pie with a pie shield if the edge of the crust is overbrowning.
Step 5
Return pie to oven; bake until custard is almost set but still slightly jiggly in the center, 15–20 minutes more. Cool pie completely before slicing, or chill pie, then bring to room temperature when ready to serve.