Preheat the oven to 350°F (175°C). Line a 9x13-inch baking pan with parchment paper, leaving an overhang for easy removal.
Make the crust: In a bowl, combine 1.5 cups all-purpose flour, 0.5 cup powdered sugar and 0.25 teaspoon salt. Stir in 0.5 cup melted unsalted butter until the mixture comes together.
Press the crust mixture evenly into the bottom of the prepared pan. Use the bottom of a measuring cup to compact it firmly.
Bake the crust for 15 to 18 minutes, or until lightly golden around the edges. Remove from the oven and reduce oven temperature to 325°F (160°C).
Prepare the filling: In a large bowl, whisk together 1.5 cups granulated sugar and 2 tablespoons cornstarch. Add 4 eggs and whisk until smooth. Stir in 0.75 cup fresh lemon juice, 2 tablespoons lemon zest, 0.5 cup heavy cream and 1 teaspoon vanilla extract until fully combined.
Pour the lemon filling evenly over the warm crust and return the pan to the oven.
Bake at 325°F (160°C) for 20 to 25 minutes, or until the filling is set but still slightly jiggly in the center. Do not overbake to preserve a creamy texture.
Remove from the oven and let cool to room temperature, then refrigerate for at least 2 hours (or overnight) to fully set.
Lift the chilled lemon slab from the pan using the parchment overhang. Dust the top with 0.25 cup powdered sugar, cut into 16 squares and serve chilled.
Notes
For extra tang, add an additional tablespoon of lemon juice. Store leftovers covered in the refrigerator for up to 4 days.