Preheat the oven to 350°F (175°C). Grease the 9x9-inch baking pan or line it with parchment paper for easy removal.

In a mixing bowl, combine the flour, ¼ cup of granulated sugar, and melted butter. Mix until well combined and crumbly.

Press the mixture firmly into the bottom of the prepared baking pan to form an even layer for the crust. Bake in the preheated oven for 10 minutes.

While the crust is baking, prepare the filling. In a separate mixing bowl, beat the softened cream cheese with an electric mixer until smooth and fluffy.

Add 1 cup of granulated sugar, eggs, lemon juice, lemon zest, and vanilla extract to the cream cheese. Mix until all ingredients are thoroughly combined and smooth.

Once the crust is finished baking, remove it from the oven and pour the lemon cream cheese filling on top of the crust. Spread it evenly with a rubber spatula.

Bake the bars for an additional 15-20 minutes, or until the filling is set and slightly golden.

Remove the pan from the oven and let it cool to room temperature. Once cooled, refrigerate for at least 2 hours before cutting into squares to serve.

For an extra touch, dust the bars with powdered sugar just before serving.