Add 1 1/4 cups of sugar and 4 Tbsp lemon zest to a large saucepan. Use your fingertips to rub the zest into the sugar for about 2 minutes. The mixture should become quite aromatic. Note: It's best to use a nonreactive saucepan. Some metal pans and sometimes even metal whisks can give the filling a metallic taste.
Next, add 5 large eggs, 1/4 cup AP flour, 1 Tbsp + 2 tsp cornstarch, and 1/2 tsp fine salt, and whisk together until smooth. Then whisk in 1 cup of fresh lemon juice. Mix until fully combined.
Cook on medium-low heat, stirring constantly with a wire whisk until the mixture thickens. It should be thick enough to coat the back of a spoon and keep its shape. This usually takes me 5-7 minutes.
Pour the lemon filling through a fine mesh strainer into a separate bowl to remove any bits of cooked egg, zest, or lemon seeds. This gives it a perfectly smooth texture!
Scoop 1/2 cup (145g) of the lemon filling into a small bowl and mix with 1/3 cup (100g) of your favorite strawberry jam.
Alternate spoonfuls of lemon filling and strawberry filling over the baked crust. Use a butter knife to marble the filling together, being careful not to cut into the crust.
Bake the bars at 350°F/175C° for 20-24 minutes, or until the filling is just set. To test if they're done, I like to do the shake test! When you think they're done, open the oven door and gently shake the pan. If the filling is mostly set and doesn't jiggle significantly (a tiny bit of jiggle in the center is ok), the bars are done baking.
Remove from the oven and place on a wire rack to cool fully. Once it's fully cooled, place the pan in the fridge to chill for 1 hour (or overnight).
Dust with powdered sugar, then use a sharp knife to cut the bars into 16 squares and enjoy!