Step 1: Preheat your oven to 350°F (175°C). Line a 9x13 inch baking pan with parchment paper, leaving an overhang on the sides to easily lift the bars out later. Lightly grease the parchment paper.
Step 2: In a large bowl, combine 2 cups all-purpose flour, 1/2 cup granulated sugar, and 1/4 teaspoon salt. Whisk them together until well combined.
Step 3: Add 1 cup (2 sticks) cold unsalted butter, cut into small cubes, to the dry ingredients. Using a pastry blender, your fingertips, or a food processor, cut the butter into the flour mixture until it resembles coarse crumbs. Do not overmix.
Step 4: Press the crumb mixture firmly and evenly into the bottom of the prepared baking pan. Use the bottom of a flat glass or a spatula to ensure a compact and uniform crust.
Step 5: Bake the crust for 18-20 minutes, or until it's lightly golden brown around the edges. While the crust is baking, prepare the lemon cream filling.
Step 6: In a large mixing bowl, beat 1 (8-ounce) package softened full-fat cream cheese and 1 1/2 cups granulated sugar together with an electric mixer on medium speed until smooth and creamy, about 2-3 minutes. Scrape down the sides of the bowl as needed.
Step 7: Add 4 large eggs, one at a time, beating well after each addition until just combined. Don't overmix.
Step 8: Stir in 1/2 cup freshly squeezed lemon juice, 2 tablespoons lemon zest, 1/4 cup all-purpose flour, and 1/2 teaspoon baking powder. Mix on low speed until just combined and smooth.
Step 9: Pour the lemon cream filling evenly over the warm, pre-baked shortbread crust. Gently spread it to the edges with a spatula.
Step 10: Return the pan to the oven and bake for 25-30 minutes, or until the edges are set and lightly golden, and the center is just slightly jiggly when gently shaken. The filling will continue to set as it cools.
Step 11: Remove the pan from the oven and let the bars cool completely on a wire rack at room temperature. Once cooled, place the pan in the refrigerator for at least 2-3 hours, or preferably overnight, to allow the bars to fully set and chill.
Step 12: Once chilled, use the parchment paper overhang to lift the entire block of bars out of the pan. Place on a cutting board and slice into squares or rectangles using a sharp knife. Dust with powdered sugar right before serving, if desired.