Heat the oven to 350°F (175°C). Line a 9 × 13-inch baking pan with parchment paper, leaving parchment overhang on two sides so the chilled cheesecake can be lifted out easily.

Combine the graham-cracker crumbs, sugar, and melted butter in a bowl until every crumb is evenly moistened. Press the mixture firmly across the bottom of the prepared pan.

Bake the crust for 8–10 minutes, then set it aside to cool slightly. A short pre-bake helps the crust stay sturdy beneath the soft cheesecake filling.

Beat the softened cream cheese and sugar until smooth, then mix in the vanilla extract. Scrape the sides and bottom of the bowl so no cream cheese lumps remain.

Add the eggs one at a time, mixing on low speed only until each one is incorporated. Avoid overbeating, since excess air can contribute to cracks as the cheesecake bakes.

Add the pure pumpkin, pumpkin-pie spice, and salt, then mix until the filling is smooth and evenly colored. Do not substitute pumpkin-pie filling, which already contains sugar and spices.

Pour the pumpkin cheesecake mixture over the slightly cooled crust. Smooth the top with a spatula so the bars bake to an even thickness.

Bake for 40–50 minutes, watching for set edges and a center with a slight, gentle wobble. The middle should not look liquid, but it should not be completely firm while hot.

Cool the cheesecake completely at room temperature before covering and refrigerating it for at least 3 hours, preferably overnight. Chilling allows the filling to finish setting and makes slicing much cleaner.

Use the parchment overhang to lift the chilled cheesecake from the pan. Cut it into 24 bars with a sharp knife, wiping the blade between cuts, and garnish each piece if desired.