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To make the dough: In the bowl of a stand mixer fitted with the flat beater attachment or working in a large bowl with an electric hand mixer, cream the butter and sugar until light and fluffy, about 3 to 5 minutes at medium speed.
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Beat in the boiled cider, followed by the egg and vanilla and continue mixing until combined. Stop the mixer and scrape the sides and bottom of the bowl.
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Add the flour, apple pie spice, baking powder, and salt and mix until a dough forms and there are no visible streaks of flour.
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Transfer the dough to a small bowl and chill, covered, in the refrigerator for at least 4 hours, or overnight.
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To bake the snickerdoodles: Once the dough has chilled, preheat the oven to 375°F with racks in the upper and lower thirds. Lightly grease 2 baking sheets or line them with parchment.
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To make the coating: In a small bowl or medium zip-top bag, mix the sugar and apple pie spice until well blended.
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Scoop the cookie dough into 2-tablespoon portions (about 36g each) and roll into balls; a jumbo cookie scoop works well here. Working with one piece at a time, transfer the portioned dough into the bowl or bag and roll or toss in the coating until completely covered.
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Arrange the cookies on the prepared baking sheets, spacing them at least 2" apart. Sprinkle the remaining coating on top of the cookies (you’ll use about 1/8 teaspoon per cookie).
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Bake the cookies for 12 to 15 minutes, swapping the position of the pans (top to bottom and back to front) halfway through. The cookies are done when they're domed, with fully set, golden brown edges; the center of each cookie should still be soft.
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Remove the cookies from the oven and allow them to cool completely on the baking sheet.
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Storage information: Store leftover apple cider snickerdoodles, covered, at room temperature for several days; freeze for longer storage.
