Preheat the oven to 350 degrees. Line an 8x8-inch baking pan with parchment paper, leaving some overhang on the sides to make it easier to remove from the pan.
Using a food processor, add the graham crackers and blend until they form fine crumbs. Add the crumbs to a small bowl, then add the sugar and salt, and mix until well combined. Add the melted butter and stir until all the crumbs are evenly moistened. It will look like wet sand.
Press the graham cracker mixture firmly into the prepared pan, using the bottom of a measuring cup or glass to create an even crust. Bake for 10 minutes, then remove from the oven to cool slightly. Keep the oven temperature at 350°F.
In a large bowl, whisk together the sweetened condensed milk, lemon zest, lemon juice, egg yolks, salt, and vanilla extract until smooth and well combined.
Pour the filling over the cooled crust. Bake for 25–30 minutes, or until the edges are set and the center very slightly jiggles.
Let the bars cool completely at room temperature. Then transfer them to the refrigerator and chill for 6–8 hours.
Use the parchment overhang to lift the bars from the pan. Slice into squares, dust with powdered sugar (optional), and enjoy!