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Preheat the oven to 350°F. Lightly grease a 9" square pan, or line with a parchment paper "sling" and spray with nonstick spray.
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For the bars: In a large bowl, beat together the butter, sugar, and salt until soft. Add the egg and boiled cider, beat until fluffy.
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Add the apple (or pumpkin) butter and mix to combine.
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In a separate bowl, whisk together the flour, baking soda, dried apples, and nuts. Stir into the butter mixture. Scrape the bowl and mix for 30 seconds more.
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Spread the batter in the prepared pan.
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Bake for 25 to 35 minutes, or until a cake tester inserted in the center comes out clean. Remove from the oven and cool on a rack.
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Once cool, loosen the edges and use the sling to pull the slab out of the pan to cut and glaze.
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For the glaze: Stir together the confectioners' sugar, cinnamon, and salt.
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Add the boiled cider (or milk) and stir until smooth, adding a few drops more milk as needed to achieve a good consistency for drizzling.
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Drizzle over each square to glaze.
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Store, covered, for 5 days on the counter. Freeze for up to a month.