Prepare your baking pan by lining an 8×8 inch baking dish with parchment paper, leaving overhang on the sides for easy removal later. Preheat your oven to 325°F (165°C).
Make the graham cracker crust by combining graham cracker crumbs, sugar, melted butter, and salt in a medium bowl. Mix until the texture resembles wet sand and all crumbs are moistened.
Press the crust mixture firmly into the bottom of your prepared pan, using the bottom of a measuring cup to compact it evenly. Bake for 10 minutes until just beginning to turn golden. Remove from oven but keep the oven on.
Beat the cream cheese and sugar in a large bowl using an electric mixer on medium speed until completely smooth and fluffy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Add eggs one at a time, beating well after each addition. Mix in the lemon juice, lemon zest, and vanilla extract until just combined.
Fold in the flour and salt gently with a spatula until incorporated, being careful not to overmix. The filling should be silky smooth with no lumps.
Pour the filling over the pre-baked crust and smooth the top with a spatula. Tap the pan gently on the counter a few times to release any air bubbles.
Bake for 35-40 minutes until the edges are set but the center still has a slight jiggle when you gently shake the pan. The bars will continue to set as they cool.
Cool completely at room temperature for about 1 hour, then refrigerate for at least 3 hours or overnight for the best texture and flavor development.
Cut into squares using a sharp knife dipped in hot water and wiped clean between cuts. Dust with powdered sugar just before serving if desired.