Heat the oven to 350°F. Place an 8-inch round springform pan on a rimmed baking sheet and set it aside.

In a food processor, pulse the gingersnap crumbs, kosher salt, and cinnamon until combined. Drizzle in the melted butter and pulse just until the crumbs are evenly moistened and hold together when squeezed.

Transfer the crumb mixture to the prepared pan and press it into a flat, even layer across the bottom. Bake for 5 minutes, then remove and set aside to cool slightly.

In the bowl of a stand mixer fitted with the paddle attachment, beat the softened cream cheese and cane sugar on medium-low speed until smooth, creamy, and free of lumps. Scrape down the sides and bottom of the bowl with a spatula as needed.

With the mixer on low speed, beat in the eggs one at a time, mixing just until incorporated after each addition. Add the vanilla extract and orange zest and mix briefly to combine.

Pour the filling over the cooled crust and use an offset spatula to smooth the top into an even layer. Gently tap the pan on the counter two or three times to release any trapped air bubbles.

Drop small spoonfuls of cranberry sauce over the filling, then drag a toothpick or skewer through the sauce in a spiral or figure-eight motion to create swirls.

Bake on the rimmed baking sheet for 30 to 35 minutes, until the sides look set and are just beginning to take on a little color. The center should still have a slight jiggle; it will continue to set as it cools.

Remove the cheesecake from the oven and let it cool completely to room temperature. Then transfer it to the refrigerator and chill for at least 2 to 3 hours, until fully cold and firm.

When ready to serve, remove the sides of the springform pan, slice, and serve chilled. Store leftover slices covered in the refrigerator for up to 3 days.

In a medium saucepan over low heat, combine the cranberries, cane sugar, and orange juice. Cook, stirring occasionally, for about 10 minutes, until the sugar has dissolved and the cranberries just begin to soften.

Increase the heat to medium, add the cinnamon stick, and continue cooking for 10 to 15 minutes, until the cranberries burst and the sauce thickens. Remove from the heat and cool to room temperature.

Use the sauce as is for a chunky texture, or puree it until smooth before swirling into the cheesecake. The sauce can be made ahead and stored in a covered container in the refrigerator for up to several days.