Set the butter in a light colored frying pan over medium heat. Cook as the butter melts and begins to sputter. Small panko-like bits will fall to the bottom, keep cooking and stirring while those bits turn brown. The butter will smell nutty and it will stop sputtering, going silent as all of the water has evaporated and the milk solids have turned a toasty brown color. Pour into a small bowl, scraping up all the brown bits from the pan, and let cool.
Make and bake the crust
Using a food processor, grind the graham crackers (225g) into fine crumbs then set them in a bowl. Into the bowl add the powdered sugar (2 tablespoons) and a pinch of salt. Into the bowl pour the liquid from the brown butter, leaving the brown butter bits in its smaller bowl (these bits should be about a half tablespoon and will go into the filling). Stir the butter and crumbs together until the mixture resembles wet sand and it clumps if you squeeze it. Press the crumbs into the bottom and up the sides of a 9 inch metal pie pan. Use a measuring cup to help you pack them into an even layer. Preheat the oven to 350 F and bake the crust for 10 minutes, this helps it set so it won’t be overly crumbly when sliced. Let cool completely.
Make the brown butter pumpkin cheesecake filling
Into the bowl with the still warm brown butter bits, add the pumpkin spice (1 tablespoon). Set the pumpkin puree (150g) in a cheesecloth or layer 2-3 paper towels (they tear if squeezed too hard) and squeeze out the excess water from the puree, we don’t want that water in the cheesecake batter. In a large bowl, add the softened cream cheese (two bricks) and use a wooden spoon or rubber spatula to press the cream cheese into the bowl. This helps remove lumps. To the bowl add the squeezed out puree, the spiced brown butter bits, the vanilla, and salt. Use a hand mixer to beat this mixture together until well mixed. Add the brown sugar (67g or ⅓ cup) and the powdered sugar (86g or ⅔ cup) and beat to mix. Pour in the heavy cream and beat the mixture until you have stiff peaks: as the beaters run through the filling they will leave ridges that do not slop over but hold shape. Pour the batter into the cooled crust and smooth into an even layer. Chill the cheesecake for at least six hours so that it sets firm enough to slice. Serve with caramel sauce. Store leftovers in the fridge, the cheesecake will keep for 3-5 days.