Preheat the oven to 350?F.
In a large sautÈ pan, melt 3 tablespoons of the butter. Add the granulated sugar, 1/2 cup of the brown sugar, the lemon juice, and 1 tablespoon of the flour. Stir the mixture for 1 minute to dissolve the sugars. Add the apples and cook, stirring, for 3 minutes. Stir in the pecans and cook for 1 minute. Add the Calvados and carefully flambÈ the apples. Cook, stirring, for 1 minute. Sprinkle with the nutmeg, cinnamon, and a pinch of the salt. Mix thoroughly, then remove from the heat. Set aside and let cool.
In a large mixing bowl, combine the remaining 4 tablespoons butter, the remaining 1/2 cup brown sugar, the remaining 1 cup flour, and the remaining pinch salt. Using your hands, blend well, until the mixture resembles coarse crumbs.
Fit the rolled-out dough into a 10-inch pie pan, trimming the edges. Pour the apple filling into the pie shell. Sprinkle the crumb mixture evenly over the top, then bake until the top is lightly browned, about 45 minutes. Remove from the oven and sprinkle the cheese over the top. Return the pie to the oven and bake until the cheese is melted and bubbly, about 8 minutes. Serve warm with vanilla ice cream.
Yield: one 10-inch pie; 8 servings