Prep the pan: Line the bottom of a 9-inch springform pan with parchment. Lightly grease the sides.
This makes slicing and serving clean and easy.
Make the crust: In a bowl, mix the cracker crumbs, sugar, and salt. Pour in melted butter and stir until the mixture looks like wet sand and holds together when pressed.
Press and chill: Firmly press the crumb mixture into the bottom of the pan, pushing it slightly up the sides. Use the bottom of a measuring cup for an even layer.
Chill while you make the filling.
Cook the blackberry swirl: In a small saucepan, combine blackberries, sugar, and lemon juice. Cook over medium heat, stirring and mashing until the berries break down and release their juices, 5–7 minutes.
Thicken the sauce (optional but helpful): If you want a thicker swirl, mix cornstarch with 1 tablespoon water and stir it into the berries. Simmer 1–2 minutes until glossy.
Remove from heat.
Strain (optional): For a smoother swirl, press the sauce through a fine sieve to remove seeds. Let it cool to room temperature. You’ll want it pourable, not hot.
Whip the cream: In a cold bowl, beat heavy cream to stiff peaks.
Don’t overbeat. Set aside.
Make the cheesecake base: In a separate bowl, beat softened cream cheese until completely smooth and fluffy, 2–3 minutes. Add powdered sugar, sour cream (or yogurt), vanilla, lemon zest, and a pinch of salt.
Beat until silky and lump-free.
Fold it together: Gently fold the whipped cream into the cream cheese mixture in two additions until no streaks remain. The mixture should be light and mousse-like.
Assemble: Spoon half the cheesecake filling onto the chilled crust and smooth the top. Drizzle a few spoonfuls of blackberry sauce over it and swirl with a skewer or knife.
Add the remaining filling and smooth again.
Top swirl: Dot more blackberry sauce on top and gently swirl to create a marbled look. Reserve any extra sauce for serving.
Chill to set: Cover the pan and refrigerate for at least 6 hours, preferably overnight. The longer chill gives a cleaner slice and better texture.
Unmold and garnish: Run a thin knife around the edge before releasing the springform.
Top with fresh blackberries, a little whipped cream, and mint if you like.
Serve: Slice with a sharp knife. For clean cuts, wipe the knife between slices. Spoon extra blackberry sauce over slices to finish.