Heat the oven to 350°F. Keep a 9-inch springform pan or a cheesecake pan with a removable bottom nearby.

In a food processor, pulse the gingersnap crumbs, salt, and cinnamon until combined. Add the melted butter and pulse again just until the crumbs are moistened and look like wet sand.

Press the crumb mixture into an even layer in the prepared pan. Bake for 5 minutes, then set the crust aside to cool.

Place the softened cream cheese and cane sugar in the bowl of a stand mixer fitted with the paddle attachment. Beat on medium-low until smooth, light, and creamy, stopping to scrape the bowl and paddle as needed.

Add the eggs one at a time, mixing on low after each addition. Blend in the vanilla and orange zest just until combined.

Pour the filling over the cooled crust and smooth the top with an offset spatula. Tap the pan firmly on the counter a few times to release any trapped air bubbles.

Drop spoonfuls of cranberry sauce across the top of the filling, then drag a toothpick or small skewer through it to make swirls.

Place the pan on a rimmed baking sheet. Bake for 30 to 35 minutes, until the edges look set and just start to brown and the center still wiggles slightly.

Let the cheesecake cool to room temperature on a wire rack, then refrigerate it for 2 to 3 hours, or until thoroughly chilled and set.

Remove the pan collar or base just before serving. Serve chilled; this is best on the first day but keeps in the fridge for 2 to 3 days.

Combine the cranberries, cane sugar, and orange juice in a medium saucepan. Cook over low heat, stirring occasionally, for about 10 minutes, until the sugar dissolves and the berries start to soften.

Raise the heat to medium and add the cinnamon stick. Keep cooking for 10 to 15 minutes, until the cranberries burst and the sauce thickens. Cool completely before using.

Use the sauce chunky or puree it in a blender or food processor until smooth. The sauce can be prepared in advance and refrigerated for several days.