Preheat your oven to 350°F (175°C). Grease the baking pan or line it with parchment paper for easier removal.
In a mixing bowl, combine the flour, softened butter, sugar, and salt for the crust. Use an electric mixer or your hands to blend until the mixture resembles wet sand.
Press the crust mixture evenly into the bottom of the prepared baking pan. Bake in the preheated oven for about 15 minutes or until lightly golden. Remove from oven and let cool slightly.
While the crust is cooling, prepare the filling. In a clean mixing bowl, beat the softened cream cheese and sugar together until smooth and creamy.
Add the eggs one at a time, mixing well after each addition. Then, stir in the fresh lemon juice, lemon zest, and vanilla extract until everything is well combined.
Pour the lemon filling over the cooled crust and spread evenly. Return to the oven and bake for an additional 25 minutes or until the filling is set and a toothpick inserted in the center comes out clean.
Remove from the oven and let the bars cool at room temperature, then refrigerate for at least 2 hours before cutting into squares and serving.
For added flavor, you can sprinkle powdered sugar on top before serving.
These bars can be stored in the refrigerator for up to a week.