Position a rack in the middle of the oven. Preheat the oven to 350°F.

Pulse the cookies and brown sugar in a food processor until the crumbs are fine. Transfer crumbs to a medium bowl; add the melted butter. Combine thoroughly, first with a spoon and then with your fingers, until the mixture is evenly moist and stays together when you squeeze it with your hand.

Press the mixture evenly over the bottom and partway up the sides of a 9-inch springform pan. Chill for 5 minutes and then bake for 10 minutes. Let the crust cool completely. Leave the oven on.

Bring a large pot of water to a boil.

In the meantime, beat the cream cheese until smooth. In a separate bowl, whisk together the brown sugar, cinnamon, ginger, allspice, nutmeg, and salt. Add this mixture to the cream cheese. Beat until thoroughly combined, scraping down the sides and bottom of the bowl as needed. Add the eggs and yolks one at a time. Make sure each egg is well incorporated before adding the next egg. Scrape down the bowl after each. Stir in the vanilla and pumpkin.

Wrap the bottom of the springform pan in two layers of aluminum foil. Pour the batter into the cooled crust. The batter will come up past the crust and will fill the pan to the rim. Tap the pan gently once or twice on the counter to release any air bubbles.

Set the pan in a larger baking dish or roasting pan, then add enough hot water to come about halfway up the sides of the springform pan. Carefully place the pan in the oven. Bake until the top of the cake looks deep golden and the center is set (the cake may just barely begin to crack), approximately 1 hour 35 minutes to 1 hour 45 minutes. The cake will jiggle a little bit when tapped. The top may rise a bit but will settle as it cools.

Turn the oven off. Leave the door ajar and let the cheesecake cool to room temperature in the oven. Once it is cooled, cover and chill overnight.