Make the Crust: Preheat oven to 325 degrees F. Line an 8-inch square baking dish with aluminum foil, allowing excess to hang over the edges of the pan; lightly grease the foil.: Preheat oven to 325 degrees F. Line an 8-inch square baking dish with aluminum foil, allowing excess to hang over the edges of the pan; lightly grease the foil. : You will notice the kitchen warming slightly as the oven comes to temperature, and the act of lining the pan ensures the finished bars lift out cleanly, leaving you with neat squares. Take care to press the foil into corners smoothly so the crust presses evenly later. One common mistake is skipping the greasing step, which can cause the foil to stick and tear, making removal messy. Using foil with overhang gives you a reliable handle to lift the whole pan, which preserves the edges of the bars while keeping them neat.
In a medium bowl, stir together the graham cracker crumbs, brown sugar, flour and salt to combine. Drizzle the melted butter over the mixture and use a fork to mix it until the entire mixture is moistened. Turn the mixture out into the prepared pan and press into an even layer. Bake until the crust starts to brown, 12 to 15 minutes. Remove from oven and set aside.: As you stir, breathe in the warm, toasty scent of the graham crackers mingling with the caramel notes of light brown sugar . The texture should be evenly moistened, with no dry pockets. Pressing firmly and evenly with the bottom of a measuring cup helps create a compact crust that bakes up crisp around the edges. Watch for subtle color change at the edges to know it is ready; underbaked crust can collapse under the filling, while overbaking will make it too hard to bite.
Meanwhile, with an electric mixer on medium-high speed, beat the cream cheese until smooth, about 2 minutes. Add the granulated sugar and beat until it is completely incorporated. Add the eggs one at a time, mixing after each addition until well combined. Add the sour cream and vanilla extract and mix until incorporated. Pour the batter over the baked crust.: The sound of the mixer will become a steady hum as the cream cheese transforms from lumpy to silky; scraping down the bowl ensures there are no stubborn pockets. The batter should be glossy and pourable when ready, smelling faintly tangy from the sour cream and sweet from the granulated sugar . Be mindful not to overbeat once the eggs are added, as too much air leads to cracks or an uneven top. A common mistake is using cold cream cheese , which results in lumps, so allowing it to reach room temperature is essential.
Using a spoon, drop dollops of the strawberry jam all over the surface of the cheesecake batter, then use a toothpick or skewer to gently swirl the jam into the batter. Bake until the edges are set but the center still jiggles slightly, 35 to 40 minutes. Allow the cheesecake to cool completely on a wire rack, about 2 hours. Cover and refrigerate until thoroughly chilled, at least 3 hours. Lift the cheesecake out of the pan and slice into bars. Leftovers can be stored in the refrigerator, in an airtight container, for up to 3 days.: As you dot the top with seedless strawberry jam , you will see bright red islands on the pale filling, and the gentle swirling motion creates marbled veins that look elegant and homemade. The baked aroma is subtle and sweet, and testing for doneness by the slight jiggle at center ensures a creamy, not overcooked interior. Cooling on a wire rack helps release steam so the texture stabilizes, and chilling firms the bars for clean slicing. A common pitfall is slicing too soon, which yields squishy pieces, so patience during the chill stage pays off in neat, satisfying bars.