Heat the oven to 350°F. Grease and line a 9-inch springform pan with parchment paper, making sure to cover the seam. Wrap the pan with heavy-duty foil or place it in a silicone cover. This will prevent water from the water bath from leaking into the crust.
Crush the ginger snap cookies and brown sugar in a food processor until the mixture has become finely ground crumbs. Slowly pour in the melted butter while the processor runs at low speed until the crumbs start to stick together.
Press the crumb mixture firmly into the bottom and sides of the prepared pan. Bake the crust for 10-15 minutes or until fragrant. Remove the crust from the pan, and reduce the oven temperature to 325°F.
In a small glass bowl, combine the espresso powder and water and stir until the espresso powder has dissolved. Let it rest while you start on the cheesecake filling.
In a large mixing bowl, use an electric mixer to blend the cream cheese, sugar, and brown sugar until smooth. Add the pumpkin puree, pumpkin pie spice, and vanilla, and continue blending until smooth. Then, add the eggs one at a time, making sure that each one is completely incorporated before adding the next. Do not overmix the filling once the last egg has been added.
Remove 1 cup of the pumpkin cheesecake batter, and stir it into the prepared espresso. Make sure it's completely mixed with no streaks of espresso. Set aside.
Spoon the pumpkin cheesecake filling over the baked crust. Then, spoon 1 ½ tablespoons of the espresso cheesecake filling on top of the cheesecake filling, and use a toothpick to swirl the fillings together.
Place the cheesecake in the middle of a large roasting pan (at least 16x13 inches), then pour about 6-8 cups of freshly boiled water into the pan, about halfway up the sides of the cheesecake pan.
Bake the cheesecake on the middle rack for 1 hour and 15 minutes, or until the sides are set and the middle is only slightly jiggly. Turn off the oven and leave the cheesecake inside for 1 hour.
Take the cheesecake out of the water bath, and let it cool completely on a wire rack. About 1 more hour.
Cover the cheesecake with plastic wrap, and chill for at least 4 hours.
When you are ready to serve, run a thin knife around the edge of the cheesecake, and carefully remove the outside ring of the pan. Transfer the cheesecake to a cake stand or large plate, and top with freshly made whipped cream and ground cinnamon, if desired, or leave plain so everyone can enjoy the swirls on top.