Prep the pan. Line a 9-inch (23 cm) springform pan with parchment on the bottom. Lightly grease the sides, then line with a strip of parchment for easy release.
Make the crust. Pulse crackers into fine crumbs. Stir in sugar (if using), salt, and melted butter until the mixture feels like wet sand.
Press firmly into the bottom of the pan, packing it tight with the bottom of a glass. Chill 15 minutes.
Cook the strawberry puree (optional but recommended for vibrant color). Blend strawberries, sugar, and lemon juice until smooth. If you want a thicker swirl, whisk in cornstarch.
Simmer 3–5 minutes, stirring, until slightly thickened and glossy. Cool completely.
Whip the cream. In a cold bowl, beat heavy cream to stiff peaks. Set aside in the fridge.
Beat the base. In a separate bowl, beat cream cheese until smooth and fluffy, about 2 minutes.
Add powdered sugar, vanilla, lemon zest, and salt. Beat until silky and lump-free.
Blend in the tangy element. Mix in Greek yogurt or sour cream just until combined for a gentle tang and lighter texture.
Fold gently. Using a spatula, fold the whipped cream into the cream cheese mixture in 2–3 additions. Keep it light to preserve airiness.
Assemble the layers. Spread half of the cheesecake filling over the chilled crust.
Dollop a few spoonfuls of strawberry puree and swirl lightly with a skewer. Add the remaining filling and smooth the top. Spoon more puree on top and create a marbled pattern.
Don’t over-swirl.
Freeze. Cover tightly with plastic wrap and foil. Freeze for at least 6 hours, preferably overnight, until firm enough to slice cleanly.
Unmold and garnish. Let the cheesecake sit at room temperature for 10–15 minutes. Release the springform collar, peel off parchment, and transfer to a serving plate.
Garnish with sliced strawberries, white chocolate curls, or mint.
Slice smart. Warm a sharp knife under hot water, wipe dry, and cut clean slices. Repeat between cuts for neat edges.