Preheat your oven to 350°F (175°C). Position the rack in the center of the oven. Line a 9x13-inch baking pan with parchment paper, leaving a 2-inch overhang on the sides so you can lift the bars out easily.

In a large bowl, beat the softened butter and 1/2 cup powdered sugar together with a hand mixer or stand mixer on medium speed for about 2 minutes, until the mixture is pale and fluffy.

Add 2 cups of all-purpose flour and 1/4 teaspoon salt. Mix on low speed for 1–2 minutes until the dough just comes together. It will look crumbly but should hold when pressed between your fingers. Checkpoint: You are ready to move on when the dough holds its shape when pinched.

Transfer the dough to your prepared pan. Using your hands or the bottom of a flat measuring cup, press it into an even, flat layer across the entire bottom of the pan. The layer should be about 1/4 inch thick.

Bake the crust at 350°F for 18–20 minutes, until the edges are lightly golden and the center looks set and dry (not shiny). Remove from the oven but do not turn the oven off. Checkpoint: You are ready to move on when the crust edges have turned a light golden-cream color.

While the crust bakes, place 1 cup of fresh raspberries in a blender or food processor and puree until smooth (about 30 seconds). Press the puree through a fine mesh sieve into a large bowl using the back of a spoon. Discard the seeds. You should have about 1/3 cup of smooth raspberry puree.

To the raspberry puree, add the 4 eggs, 1 1/2 cups granulated sugar, 1/2 cup fresh lemon juice, 1 tablespoon lemon zest, 1/3 cup all-purpose flour, 2 tablespoons raspberry jam, 1/4 teaspoon baking powder, and a pinch of salt. Whisk everything together vigorously for about 1 minute until completely smooth. The mixture will be a beautiful rosy-pink color.

Pour the filling mixture directly over the hot crust as soon as it comes out of the oven. Carefully transfer the pan back to the oven.

Bake at 350°F for 22–25 minutes, until the filling is set around the edges and only has a very slight jiggle in the very center (like Jell-O, not liquid). It will firm up more as it cools. Do not overbake — the top should not crack or brown. Checkpoint: You are ready to move on when the edges are fully set and the center jiggles just slightly when you gently shake the pan.

Remove the pan from the oven and let it cool at room temperature for 30 minutes. Then transfer to the refrigerator and chill for at least 2 hours (or up to overnight) until completely firm and cold.

Once fully chilled, lift the bars out of the pan using the parchment paper overhang. Place on a cutting board. Dust generously with powdered sugar through a fine sieve. Slice into 16 bars using a sharp knife, wiping the blade clean between cuts for neat edges.