Preheat your oven to 350°F (175°C). Grease an 8x8 inch baking dish or line it with parchment paper for easy removal.
In a medium mixing bowl, whisk together the flour, powdered sugar, cornstarch, and salt until well combined.
Pour the melted butter into the dry ingredients and mix until crumbly. Press this mixture evenly into the bottom of the prepared baking dish to form the crust.
Bake the crust in the preheated oven for about 15-20 minutes, or until it lightly golden. Remove it and let it cool slightly.
In a separate large bowl, combine the Greek yogurt, granulated sugar, eggs, lemon juice, lemon zest, and vanilla extract. Whisk until the mixture is smooth and creamy.
Pour the yogurt filling over the slightly cooled crust, spreading it evenly.
Return the pan to the oven and bake for an additional 25-30 minutes, or until the filling is set and just firm to the touch.
Remove from the oven and allow to cool completely at room temperature, then refrigerate for at least 2 hours to set fully.
Once set, cut into squares and dust with powdered sugar if desired.
Notes
Serve on a pretty plate or a rustic wooden board, and garnish with thin lemon slices or a sprig of fresh mint for a fresh touch.