Add the pumpkin puree, brown sugar, 1 teaspoon of pumpkin pie spice, apple cider vinegar, and ¼ teaspoon salt to a saucepan and stir well. Simmer on low for about 25 minutes, stirring often, until it's reduced by half and thickened. Let it cool completely before using it in the filling.
Melt your stick of butter in a saucepan over medium heat, swirling occasionally as it foams. Watch closely for small brown flecks to form at the bottom, which means it's ready. Pull it off the heat right away and let it cool before combining with your crumbs.
Stir the graham cracker crumbs with the remaining salt and pumpkin pie spice, then pour in the cooled browned butter. Mix until the texture resembles wet sand, then press it firmly into a parchment-lined 8x8 pan. Chill the crust in the fridge while you prepare the filling.
Beat the softened cream cheese with powdered sugar, vanilla, and a pinch of salt until completely smooth. In a separate bowl, whip the heavy cream to stiff peaks. Fold the cooled pumpkin butter into the cream cheese first, then gently fold in the whipped cream in two batches.
Pour the finished filling over your chilled crust and smooth it into an even layer with a spatula. Refrigerate overnight so it sets completely, and for the cleanest slices, pop the pan in the freezer for about an hour right before cutting and serving.