Heat the oven to 350 °F, line a 9″ x 9″ pan with parchment paper, and coat it lightly with non-stick spray. The parchment makes lifting and slicing much easier once the cheesecake is fully chilled.
Stir the graham cracker crumbs and melted butter together in a medium bowl, then press the mixture firmly and evenly into the prepared pan. It should look like wet sand before pressing, and a flat measuring cup helps create a crust that holds together cleanly.
Beat the cream cheese, sugar, sour cream, and vanilla with an electric mixer or stand mixer fitted with the paddle until smooth, about 2 minutes. Stop when the mixture looks creamy and even, with no visible lumps along the sides of the bowl.
Add the eggs one at a time, mixing after each addition just until combined. Keep the mixing gentle here so the filling stays creamy instead of turning dense or airy.
Pour the filling over the crust and bake for 40 to 45 minutes. The edges should look lightly golden and set, while the center should still wobble slightly like Jell-O.
Cool the cheesecake completely before moving on. This takes patience, but it is what gives you neat slices and the best texture instead of a soft, messy center.
For the compote, combine the strawberries, sugar, water, lemon juice, and cornstarch in a medium saucepan and bring to a bubble over medium heat, stirring every few minutes with a silicone spatula. After about 10 minutes, the mixture should thicken enough to coat the back of a spoon.
Transfer the compote to a heat-proof bowl, cover it tightly, and chill it until cool. You want it cold enough to spoon neatly onto the bars instead of running over the sides.
Lift the cooled cheesecake from the pan and cut it into even bars, trimming the edges if they browned more than you like. A cold cheesecake will slice far more cleanly than a room-temperature one.
Use a spoon to carve a shallow strip from the top center of each bar for the strawberry filling. Start shallow, because you can always remove a bit more, but you do not want to dig down to the crust.
Spoon the chilled strawberry compote into the carved center of each bar. The topping should sit in the channel rather than spill heavily over the edges.
Melt the white chocolate in 30-second intervals, stirring between each round until smooth. If it looks glossy and fluid, it is ready to drizzle.
Finish each bar with a spoonful or thin drizzle of white chocolate over the top. Once chilled, the bars should look creamy, tidy, and very close to the throwback treat people remember.