Heat the oven to 350°F (177°C) and line a 9-inch square baking pan with parchment paper, leaving enough overhang to lift the chilled bars out later. The overhang should act like handles, which makes clean removal much easier once the filling is firm.

Pulse the graham crackers into fine crumbs, or crush them in a zip-top bag with a rolling pin, then stir the crumbs with the granulated sugar and melted butter in a medium bowl. The mixture should look thick, coarse, and sandy, with no large dry chunks hiding in the bowl.

Press the crumb mixture firmly into the bottom of the lined pan. A tightly packed crust should look even from corner to corner and feel compact rather than loose.

Bake the crust for 8 minutes, then set it aside to cool briefly while you prepare the filling. The crust will smell lightly toasty and look set, which helps it stay crisp under the cheesecake layer.

Beat the cream cheese on medium speed for 1 minute until completely smooth, then add the egg, sugar, lemon zest, lemon juice, and vanilla and mix on medium speed until creamy, about 3 minutes. The batter should look thick and glossy, with no visible lumps from cold cream cheese.

Gently fold in the blueberries, then spread the filling evenly over the still-warm crust. If you are using frozen berries, keep them frozen so the batter stays pale and does not turn muddy purple.

Bake for 30 to 35 minutes until the cheesecake is set and the edges are lightly browned. The edges will look slightly puffed, and the center should still have a gentle wobble when the pan is nudged.

Cool the pan on a wire rack for 30 minutes, then refrigerate the bars for at least 3 hours. The filling will sink a little as it cools, which is normal, and the long chill is what gives you clean slices.

Lift the chilled cheesecake out by the parchment and cut into squares. The bars should feel firm and cold, not soft or warm, before the knife goes in.