Preheat your oven to 350°F (175°C). In a large mixing bowl, cream together the unsalted butter and granulated sugar until light and fluffy. Stir in the lemon zest. Gradually add in the all-purpose flour and kosher salt until just combined. Press the dough evenly into a greased 9x13-inch baking pan. Chill in the refrigerator for 15 minutes, then bake for 15-20 minutes until lightly golden. Allow to cool.

In a medium saucepan over medium heat, whisk together granulated sugar, cornstarch, and freshly squeezed lemon juice. Add in the fresh raspberries and continuously stir until thickened, about 6 minutes. Remove from heat and strain the mixture through a fine mesh sieve to remove seeds, letting it cool down while you prepare the filling.

In a mixing bowl, whisk together the large eggs, granulated sugar, lemon zest, and all-purpose flour until smooth. Gradually add in the freshly squeezed lemon juice, whisking until well combined. Pour the lemon filling over the cooled crust.

Dollop spoonfuls of the cooled raspberry puree over the lemon filling. Swirl the raspberry puree into the lemon filling using a toothpick or skewer to create a marbled effect, being careful not to disturb the crust.

Bake the bars in the preheated oven for 30-35 minutes. The filling should be set in the center and slightly jiggly when done. Remove from the oven and cool to room temperature for about 30 minutes.

Once cooled, refrigerate the bars for at least one hour to set properly before cutting. Dust with powdered sugar before serving.