Roll out the dough and fit into a 9-inch pie pan, then trim and flute the edges. Set aside.
To make the topping, put the butter, brown sugar, flour, oatmeal, walnuts, cinnamon and salt in a large bowl. Using your fingertips or a pastry blender, blend the ingredients together until the mixture looks like coarse crumbs. Don't worry about over blending the ingredients; just keep at it until you have a coarse, crumbly mixture. Set aside.
To make the filling, peel halve and core the apples, then cut them into slices 1/4" to 1/3" thick. Set aside.
In a large skillet, combine the butter, sugar and salt and place over medium-high heat. Cook, stirring frequently, until the butter has melted and blended with the sugar, 2 to 3 minutes. Add the apple slices and lemon juice. The apples will almost immediate exude some juice. (Pears, if you are using them here, will exude quite a lot of juice.) Continue to cook, stirring frequently, until the apple slices are tender and translucent and any juices have mostly evaporated, about 15 minutes. Remove from the heat and set aside to cool for about 20 minutes, stirring once or twice.
Preheat the oven to 450 F while the apples are cooling.
Spread the apples in the prepared pie shell, then sprinkle the oatmeal topping evenly over the fruit. Bake for 10 minutes, then reduce the heat to 350 F and continue baking for about 30 minutes longer, until the topping and the edges of the crust are browned. Depending on the fruit, you might also see some syrupy juices bubbling around the crust.
John Phillip Carroll, pie pie pie (Chronicle Books, 2005).
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