Prepare the pan. Wrap the outside of a greased 9-inch springform pan with a double layer of heavy-duty foil (about 18-inch square), pressing it carefully around the pan. Set on a baking sheet.

Make the crust. Combine the melted butter and crumbs in a small bowl, then press into the bottom of the prepared pan. Bake for 6 minutes, then cool on a wire rack.

Make the cranberry topping. While the crust bakes, combine the cranberries, sugar, and water in a large saucepan. Cook uncovered over medium heat for 12–15 minutes, until the berries pop. Stir in the lemon juice, then pass the mixture through a food mill into a small bowl to remove the pulp and seeds. Set aside.

Make the filling. In a large bowl, beat the cream cheese, sugar, and lemon juice until no lumps remain. Add the eggs and beat on low speed just until incorporated.

Fill and swirl. Pour the filling into the crust. Spread 60 mL (¼ cup) of the cranberry topping over the filling, then cut through with a knife to swirl. Reserve the rest of the topping for later.

Bake in a water bath. Set the springform pan into a larger pan and pour in about 1 inch (2.5 cm) of hot water. Bake for 55–65 minutes, until the centre is firm and the top looks dull rather than glossy.

Cool. Remove the springform pan from the water bath and take off the foil. Let the cheesecake cool on a wire rack for 10 minutes, then run a knife carefully around the edge of the pan to loosen it. Let cool for 1 hour more.

Top and chill. Spread the remaining cranberry topping over the cheesecake. Once completely cooled, cover and refrigerate overnight.

Serve. Remove the rim of the pan before slicing.