Set oven rack in lower-middle position and preheat to 325F. Brush a 9-inch springform pan evenly with melted butter.

In a food processor, combine graham crackers and salt and process until finely ground. Drizzle in melted butter and maple syrup and pulse to combine.

Dump the graham mixture into the prepared pan and use your fingers and the bottom of a measuring cup to press it evenly along the bottom.

Place in the oven to bake until browned and dry, about 20 minutes. Cool completely, at least 30 minutes.

In a food processor, puree the squash, cream cheese, brown sugar, maple syrup, vanilla, cinnamon, ginger, nutmeg, and salt until evenly combined. Add the cream and beaten eggs, and process until evenly combined.

Pour the filling into the baked and cooled crust. Bake at 325F until the edges are set but the center is still runny, 35 to 40 minutes.

Turn off the oven and prop open the door with a wooden spoon. Continue cooking the cheesecake in the off oven for 1 hour.

Cool fully in the fridge, at least 3 hours and preferably overnight, before serving.

For the caramel, combine sugar, corn syrup, and water in a small pot. Cook over medium heat, swirling occasionally, until deeply browned, about 10 to 12 minutes.

Carefully add the cream and espresso powder and simmer until thick and combined, about 1 minute. Cool slightly then pour over cheesecake or serve alongside slices.