There's no better way to celebrate pumpkin-spice season! With swirls of pumpkin filling, caramel and a gingersnap crust, this autumnal cheesecake is a delight. We start by whipping up a classic cheesecake batter, then add pumpkin and warm spices to half the batch. Both are used to create a unique bullseye pattern. Nutty spiced seeds add crunch. Make sure all the ingredients are at room temperature -- this ensures that the cheesecake is smooth and creamy.
Position a rack in the center of the oven and preheat to 325 degrees F.
For the crust: Add the gingersnap cookies, melted butter and salt to a food processor. Process until the crumb mixture looks like coarse sand, about 30 seconds. Press the crumb mixture into the bottom and up the sides of a 10-inch springform pan. Bake the crust until it is fragrant and golden brown, about 12 minutes.
Remove the crust to a wire rack to cool completely, about 30 minutes. Wrap the bottom and sides of the pan tightly with foil and place in a roasting pan.
For the filling: Add the cream cheese to a stand mixer fitted with the paddle attachment and beat on medium speed until smooth, about 3 minutes. Add the sugar and beat, scraping down the sides of the bowl as needed with a rubber spatula, until light and fluffy, about 2 minutes. Beat in the eggs one at a time. Add the sour cream, vanilla and salt and beat just until combined.
Scoop 3 cups of the cheesecake filling into a medium bowl. Add the pumpkin puree, cinnamon, ginger, cloves, nutmeg and 1/4 cup water and stir with a rubber spatula until well combined. Bring a pot or kettle of water to a boil.
Fill a 1-cup measure with plain cheesecake filling and pour into the center of the cooled crust. Fill a 1-cup measure with pumpkin filling and pour into the center of the plain filling. The batter will spread as you add alternating scoops, widening to form concentric circles. Repeat with the remaining batter in 1/2-cup increments alternating between flavors, until all the batter is used.
Carefully place the roasting pan in the oven (don't pull the rack out of the oven). Pour enough hot water into the roasting pan to come about halfway up the sides of the foil-wrapped pan.
Bake until the top of the cheesecake is lightly browned around the edges, but the center is still jiggly, about 1 hour 20 minutes. Turn the oven off and let the cheesecake sit in the oven until the center becomes just slightly jiggly, about 1 hour (see Cook's Note).
Carefully remove the cheesecake from the roasting pan to a wire rack. Cool to room temperature. Cover and refrigerate at least 8 hours and up to overnight.
For the spiced pumpkin seeds: Preheat the oven to 350 degrees F. Toss the pumpkin seeds, oil, sugar, cinnamon, ginger, salt and cloves in a small bowl. Spread the mixture on a baking sheet and roast until golden brown, about 10 minutes. Set aside to cool.
For the pumpkin caramel: Melt the sugar in a small saucepan over medium heat until caramelized and dark amber (a digital instant-read or candy thermometer should register 245 degrees F), about 4 minutes, stirring occasionally with a whisk. Lower the heat to low. Carefully whisk in the heavy cream and butter and continue stirring until melted, about 1 minute. Whisk in the pumpkin puree, cinnamon, salt, vanilla, ginger and cloves until combined. Remove from heat and let cool slightly before serving.
To serve: Let the cheesecake sit at room temperature 30 minutes before serving. Unlock the springform pan and remove the ring. Sprinkle the spiced pumpkin seeds around the top outer edge of the cheesecake. Dip a knife in a warm water and wipe dry before slicing each piece. Serve with a dollop of whipped cream and a drizzle of the pumpkin caramel.
With a jiggly center, the cheesecake may not appear done, but do not bake it longer. It will set further as it cools.