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Preheat the oven to 325°F with a rack in the center. Line an 8" square pan with a parchment sling and lightly grease the parchment.
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To make the crust: In a medium bowl or the bowl of a stand mixer fitted with the flat beater, beat the butter and brown sugar on medium speed until smooth, about 30 seconds. Scrape the bowl and add the flour and salt. Continue beating on low speed for about a minute until the mixture is somewhat crumbly; when you squeeze a clump in your hand, it should hold together. Transfer the crust mixture to the prepared pan and shake gently to evenly distribute. Firmly press the mixture into an even layer with your hands.
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Prick (“dock”) the dough all over with a fork.
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Bake the crust until lightly golden, 15 to 20 minutes. Remove it from the oven and increase the oven temperature to 350°F. Allow the crust to cool slightly while you prepare the filling.
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To make the filling: In a large bowl, add the apples and lemon juice and stir to combine. In a large skillet, melt the butter over medium-high heat. Add the spice and stir to combine.
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Add the apples to the skillet and stir to coat in the butter mixture. Cook for about 5 minutes, stirring occasionally, until the apples just begin to soften.
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Sprinkle the sugar evenly over the apples and stir to combine. Cook, stirring occasionally, for 6 to 10 minutes. Initially, the apples will release a lot of liquid; continue to cook until most of the liquid has evaporated. Remove from the heat once the mixture has become just slightly sticky. (The apples will not be fully tender.) Allow the apple mixture to cool in the pan off the heat while you prepare the topping.
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To make the topping: In a medium bowl, combine the flour, brown sugar, and spice. Add the butter and use your hands or a fork to work it into the flour mixture until crumbly, with most of the butter chunks the size of peas and some slightly larger chunks throughout.
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To assemble and bake the Apple Pie Bars: Transfer the cooked apples to the pan with the crust and spread them into an even layer. Sprinkle the topping evenly over the surface of the apples.
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Bake the Apple Pie Bars for 35 to 40 minutes, until the topping is light golden brown.
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Remove from the oven and allow the bars to cool completely in the pan before lifting them out to slice and serve.
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Storage information: Store any leftover Apple Pie Bars, well-wrapped, at room temperature for several days; freeze for longer storage.