Preheat your oven to 350°F (175°C). Line a 9×13-inch metal baking pan with parchment paper, letting the paper overhang the long sides to create a sling for easy removal. Lightly spray or grease the parchment and any exposed sides of the pan.

In a medium mixing bowl, whisk together 2 cups flour, 1/2 cup powdered sugar, 1/4 cup granulated sugar, and 1/2 teaspoon fine sea salt. Add the cold cubed butter and cut it into the dry ingredients using a pastry cutter, two knives, or your fingertips until the mixture resembles coarse crumbs with some pea-sized pieces of butter. Stir in the vanilla extract.

Transfer the crust mixture to the prepared pan. Press it firmly and evenly into the bottom of the pan, using your hands or the flat bottom of a measuring cup to pack it down well. Bake for 18–20 minutes, or until the edges are just turning light golden and the surface looks dry rather than shiny. Leave the oven on.

While the crust bakes, place the chopped strawberries in a small bowl with 1 tablespoon granulated sugar and let sit for 5–10 minutes to release their juices. Transfer the berries and juices to a blender or food processor and blend until smooth. For a silkier filling, press the purée through a fine-mesh strainer to remove seeds; this step is optional.

In a large mixing bowl, whisk together 1 1/2 cups granulated sugar, 1/4 cup flour, a small pinch of salt, and the finely grated lemon zest until well combined. This helps distribute the flour evenly and prevents lumps when adding the wet ingredients.

Add the eggs to the sugar-flour mixture and whisk gently just until smooth and combined, avoiding whipping in too much air. Stir in the freshly squeezed lemon juice, then mix in the strawberry purée until the filling is evenly blended. If desired, add 2–3 drops of red or pink gel food coloring for a brighter pink hue and stir to combine.

Give the filling a final stir, then carefully pour it over the hot, just-baked crust while it is still in the pan. Using the crust while it is hot helps the filling and crust layers bond and reduces separation.

Return the pan to the 350°F (175°C) oven and bake for 22–28 minutes, or until the center of the filling looks set but still has a slight wobble when you gently jiggle the pan. If the filling sloshes, continue baking for a few more minutes. The top may puff slightly during baking; it will settle as it cools.

Place the pan on a wire rack and let the bars cool completely to room temperature, about 1–2 hours. Then cover and refrigerate for at least 2 hours, or overnight, until thoroughly chilled and set. Use the parchment overhang to lift the slab from the pan. Dust generously with powdered sugar, then cut into 24 small bars or 16 larger bars. Garnish with strawberry slices or lemon wedges if desired.

Serve the strawberry lemonade bars chilled or at cool room temperature. The filling should be creamy yet firm, with a tender, buttery shortbread crust.