Preheat oven to 350°F. Line a 9×9-inch pan with aluminum foil or parchment paper.
Crush the graham crackers in a food processor or in a large ziploc bag with a rolling pin until fine crumbs form.
In a medium mixing bowl, combine crumbs, sugar, salt, and melted butter. Mix to combine. Press evenly into the bottom of the prepared pan and bake for 10 minutes.
In a large mixing bowl, beat cream cheese until smooth. Add condensed milk and mix until combined. Then, add egg yolks one at a time, mixing well after each. Mix in lime zest, juice, and vanilla extract until combined.
Pour filling over baked crust and return to oven. Bake for 15-18 minutes or until set. Avoid browning the top. Chill in the refrigerator for 2-4 hours before serving.
Cut into bars and serve. Store in an airtight container in the refrigerator for up to 5 days.