Preparation Steps

• Line a 9×13-inch metal baking pan with parchment, leaving a 2-inch overhang on the long sides for easy lifting. Preheat oven to 350°F (175°C).
• Make the berry swirl: In a medium saucepan, combine berries, 1/3 cup sugar, lemon juice, lemon zest, and water. Let stand 5 minutes to lightly macerate. Bring to a gentle simmer over medium heat, stirring and mashing larger berries as they soften, 4–6 minutes.
• Whisk cornstarch with 1 tablespoon cool water in a small bowl, then stir into the berries. Cook 1–2 minutes more, until glossy and thick enough to coat a spoon. Transfer to a shallow dish and chill until cool to the touch (about 20 minutes).
• Make the crust: In a bowl, mix graham crumbs, 3 tablespoons sugar, and salt. Stir in melted butter until evenly moistened. Press firmly into the pan in an even layer using the bottom of a measuring cup. Bake 10 minutes, then cool on a rack. Reduce oven temperature to 325°F (165°C).
• Start the cheesecake layer: In a large bowl with a hand mixer on low speed (or a stand mixer with paddle), beat cream cheese until completely smooth and no lumps remain, 1–2 minutes. Tip: If the cream cheese isn’t soft, warm the bowl over a pot of steaming (not boiling) water for 15–20 seconds and stir until silky.
• Add 3/4 cup plus 2 tablespoons sugar and cornstarch; mix on low just until incorporated, scraping bowl as needed. Blend in sour cream and vanilla on low speed until smooth.
• Lightly beat the eggs and yolk in a small bowl. With the mixer on low, stream them into the batter, mixing only until combined. Tap the bowl on the counter a few times to release air bubbles.
• Assemble: Pour the cheesecake batter over the cooled crust and smooth the top. Dollop spoonfuls of the cooled berry mixture all over the surface (you’ll use most, but reserve 2–3 tablespoons for serving if you like). Drag a butter knife through the dollops to create swirls without stirring them in completely. Firmly tap the pan on the counter 3–4 times to pop any trapped air.
• Bake at 325°F (165°C) for 28–35 minutes, until the edges are set but the center still wobbles slightly when the pan is nudged. Do not overbake.
• Cool the pan on a rack for 1 hour, then refrigerate uncovered until fully chilled and set, at least 4 hours or overnight.
• Lift the bars out by the parchment. Warm a knife under hot water, wipe dry, and slice into 16 squares, wiping the blade between cuts. Serve with the reserved berry sauce or fresh berries if desired.