Preheat oven to 350°F (175°C) and grease a springform pan with non-stick spray and parchment paper.
Blend gingersnaps into crumbs in a food processor. Add melted butter, brown sugar, and salt, and pulse until combined. Press mixture into pan and bake for 12 minutes. Let cool.
Reduce oven heat to 325°F (163°C). Beat cream cheese until smooth. Add eggs one at a time, then mix in sugar, yogurt, and vanilla.
Separate 2 cups of cheesecake batter and mix with pumpkin puree, pumpkin pie spice, and cinnamon.
Layer batters alternately in the crust, starting with plain batter, then pumpkin batter. Swirl layers gently with a toothpick.
Wrap the springform pan in foil to prevent leaks. Bake at 325°F for 30 minutes, then reduce heat to 250°F and bake for 50 more minutes.
Turn off the oven, let the cheesecake rest inside for 30 minutes, then cool with the oven door cracked for 1 hour.
Bring to room temperature (2–3 hours), then refrigerate overnight. Before serving, top with whipped cream and drizzle with caramel sauce. Slice with a wet knife.