Step 1

Position a rack in the middle of the oven and preheat to 325 degrees F. Wrap the bottom and sides of a 10-inch springform pan with 3 pieces of heavy-duty foil.

Step 2

For the crust: Add the crackers, sugar and cheddar cheese to a food processor and process until fine crumbs form, about 1 minute. Pour in the melted butter and pulse until well incorporated and the mixture holds together when pinched between your fingers, 10 to 12 pulses. Press the crumb mixture into the prepared springform pan, taking care to get the crust evenly to the edges. Bake until golden brown and set, 10 to 20 minutes. Let cool for 10 minutes then place in a large roasting pan.

Step 3

For the cheesecake: Beat the cream cheese, cheddar cheese and granulated sugar in the bowl of an electric mixer fitted with the paddle attachment on medium speed until well combined, 3 to 4 minutes. Add the sour cream and vanilla and beat until just combined. Reduce the speed to low and add the eggs, one at a time, until just combined. (Take care not to overmix or the cheesecake will puff up and crack.) Pour the batter evenly over the crust, smoothing the top. Pour enough hot water into the roasting pan to come about halfway up the sides of the foil-wrapped springform pan. Bake until the outside of the cake is set but the center is still slightly loose, about 1 hour 10 minutes.

Step 4

Turn the oven off and leave the cheesecake in the oven for another hour. Remove the cheesecake from the roasting pan to a cooling rack. Run a knife around the edge and cool to room temperature, about 2 hours. Cover and refrigerate at least 8 hours.

Step 5

Run a knife around the edge of the pan once more and unlock to unmold the cheesecake. Remove from the springform base and transfer to a serving platter or cake stand and smooth the edges with a knife.

Step 6

For the apple butter caramel: About 2 hours before serving the cheesecake, whisk the heavy cream, apple butter, corn syrup, butter, vanilla extract and salt in a small saucepan and bring the mixture to a simmer over medium heat, whisking constantly, until very smooth, 4 to 5 minutes. Remove from the heat.

Step 7

Sprinkle the brown sugar evenly in a medium skillet. Cook over medium heat, stirring with a rubber spatula, until the sugar melts and is smooth, 3 to 5 minutes. Remove from the heat and slowly drizzle in the warm cream mixture, whisking constantly. Return the skillet to medium heat and bring to a gentle simmer; cook, whisking frequently, until smooth and a deep amber color, 5 to 7 minutes. Transfer to a heat proof container and refrigerate, uncovered, until cool, about 1 hour.

Step 8

Pour the caramel sauce into the center of the cake and use an offset spatula to spread it out, letting some of the sauce drip over the sides. Store in the refrigerator for up to 1 week.