Melt 2 tablespoons of unsalted butter in a sauté pan over medium heat. Add the sliced Pink Lady apples and 2 tablespoons of sugar, stirring occasionally. Sauté for about 8-10 minutes until slightly softened.

Stir in dark rum and a pinch of salt, then spread the mixture over the blind-baked pie crust.

In a large bowl, whisk together 2 whole eggs, 2 egg yolks, 1 cup of heavy cream, ½ cup of sugar, 1 teaspoon of pure vanilla extract, nutmeg, and salt until smooth.

Pour the custard mixture over the sautéed apples in the pie crust.

Preheat oven to 325°F (163°C). Bake the pie for approximately 30 minutes until the custard is set but slightly jiggly.

In a separate bowl, mix together 1 cup of sliced almonds, 2 tablespoons of sugar, 2 tablespoons of softened butter, and a pinch of salt for the topping.

After the initial bake, sprinkle the almond topping over the custard and bake for an additional 15-20 minutes until golden brown.

Let the pie cool completely on a wire rack before serving. Optionally, chill in the refrigerator.