Step 1: Preheat your oven to 350°F (175°C). Line a 9×13-inch baking dish with parchment paper, leaving an overhang on the sides. Lightly grease the parchment paper.
Step 2: In a large bowl, whisk together the flour, 1/2 cup granulated sugar, and 1/4 teaspoon salt. Cut in the cold butter using a pastry blender or your fingertips until the mixture resembles coarse crumbs.
Step 3: Press the crumb mixture evenly into the prepared baking dish. Use the bottom of a flat glass or measuring cup to compact it firmly. Bake for 15-20 minutes, or until lightly golden brown. Let cool completely on a wire rack.
Step 4: In a medium saucepan, whisk together 1 1/2 cups granulated sugar and cornstarch until well combined.
Step 5: Gradually whisk in the lemon juice, lemon zest, and water until smooth. Place over medium heat and cook, stirring constantly, until the mixture thickens to a pudding-like consistency and comes to a gentle boil (5-7 minutes).
Step 6: Remove from heat. Whisk in the egg yolks one at a time, ensuring each is fully incorporated. Stir in the 1/4 cup butter until melted and smooth.
Step 7: Pour the hot lemon filling evenly over the cooled crust. Spread gently. Cover loosely with plastic wrap and refrigerate for at least 2-3 hours, or until completely set.
Step 8: In a large mixing bowl, beat the softened cream cheese and 1/2 cup softened butter with an electric mixer until smooth and creamy (2-3 minutes).
Step 9: Gradually add the powdered sugar, beating until light and fluffy. Add the vanilla extract and pinch of salt, then beat for another minute until well combined and airy.
Step 10: Once the lemon layer is set, remove the baking dish from the refrigerator. Evenly spread the cream cheese topping over the chilled lemon layer.
Step 11: Refrigerate the bars for at least another hour to allow the topping to set and flavors to meld. For best results, chill thoroughly before cutting.
Step 12: Use the parchment paper overhang to lift the bars out of the pan. Place on a cutting board and slice into desired squares or rectangles. Serve cold. Store leftovers in an airtight container in the refrigerator for up to 3-4 days.