Lightly spray a 9x13-inch baking pan with cooking spray. Using a mixer fitted with a paddle attachment, cream the butter and sugar together on medium speed (about 2 minutes) until light in color. Add the lemon zest and mix for a few seconds.
Combine the flour and salt in a separate bowl. With the mixer on low, add the flour mixture to the butter until just mixed, about 1 minute. Place the dough onto a well-floured board and gather into a ball and transfer to the baking pan. Using your fingers, evenly press and flatten the dough into the baking pan.
Chill the dough for 15 minutes. Bake the crust for 15 to 20 minutes, until very lightly browned. Cool the crust in the baking sheet on a wire rack for about 30 minutes, until the dough is slightly firm. Keep oven heated to 350°F.
Put the sugar, cornstarch, and lemon juice in a small saucepan and whisk together. Add raspberries to the saucepan. Cook over medium heat, constantly whisking until the puree has broken down and thickened and has come to a bubble, about 6 minutes. Strain the hot thickened puree, discarding the seeds. Set the strained puree aside, at room temperature until ready to use.
To make the filling, whisk together the eggs, sugar, lemon zest, and flour until combined. Gradually add the lemon juice and whisk until combined and pour over the crust. Add about a tablespoon-sized spoonfuls of raspberry puree around the entire surface of the lemon mixture. Quickly drag a toothpick across the surface to create swirls.
Carefully transfer to the oven. Bake for 30-35 minutes until the filling is set in the center. Let cool to room temperature.
Cut into squares or triangles and dust with confectioners' sugar.