Special equipment: A 10-inch springform pan
For the crust: Adjust an oven rack to the middle position and preheat the oven to 325 degrees F.
Put the graham crackers in a food processor and pulse until fine crumbs, about 2 1/2 cups.
Brush a 10-inch spring form pan with some of the butter. Add the graham cracker crumbs the remaining butter, 1/4 cup of the sugar and a pinch of salt to a medium bowl and stir to combine. Press the crumb mixture into the bottom and 1 inch up the side of the pan. Use the back of a measuring cup or drinking glass to pack the crust firmly and evenly in to the edges of the pan. Bake until the crust is lightly crisp and set, 15 to 20 minutes. Cool completely, then set the pan on top of a large sheet of aluminum foil and wrap the foil around the bottom of the pan and up the sides. Place the springform in a roasting pan.
For the filling: Bring a large pot of water to a boil. Whip the cream cheese in the bowl of a stand mixer fitted with a paddle attachment until smooth. Add the remaining sugar and beat until just light and fluffy, scraping down the sides of the bowl and the paddle attachment as needed, about 2 minutes. Add the sweet potato puree, sour cream, eggs, vanilla, ground cinnamon and salt and beat until just combined. Scrape the filling into the cooled crust.
Carefully pour boiling water into the roasting pan so that it goes half-way up the sides of the springform pan, being careful not to get any of the water in the springform pan. Bake until the edges of the cheesecake are set but the center still jiggles when the pan is tapped, about 2 hours. Turn off the oven and open the oven door for 1 minute to let out some heat. Close the oven door and leave the cheesecake in the oven for 1 hour more. Carefully remove the cheesecake from the roasting pan, remove the foil and cool on a wire rack. Run a thin knife or spatula around the edges of the cake to release it from the sides, (this also helps reduce cracks in the top of the cake as it chills). Cover the pan with plastic wrap and refrigerate the cheesecake 8 hours or overnight.
For the s'more topping: Once the cheesecake has chilled completely, put the semi-sweet chocolate chips in a medium bowl. Heat the heavy cream in a small saucepan over medium heat until it just comes to a simmer, about 2 to 3 minutes. Pour the hot cream over the chocolate chips and let stand for 1 minute, then stir the cream and chocolate together until completely smooth. Set aside to cool to room temperature.
Position a rack in the center of the oven and preheat the broiler to high. Pile the miniature marshmallows on top of the cheesecake in as even of a layer as possible (it's okay if some marshmallows overlap). Place the cheesecake on a baking sheet, then broil until the tops of the marshmallows are lightly golden brown, about 1 minute. Keep the oven door slightly open and rotate the pan as needed to get even browning.
Run a thin knife or spatula between the cake and the pan to release it from the sides. Unlock the pan and remove the ring. Spray both sides of a sharp knife with non-stick cooking spray and slice the cake into 10 even slices, spraying the knife between each slice to keep the gooey marshmallows from sticking to the knife. Drizzle each piece of cheesecake with the cooled chocolate sauce and serve.
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