Heat the oven to 350°F (175°C). Line a 9 x 13-inch baking pan with parchment paper, leaving an overhang on the long sides so the cooled bars can be lifted out easily.

Beat the softened butter and granulated sugar until creamy. Add the egg and vanilla extract, then beat until the mixture is smooth and well combined.

In a separate bowl, whisk together the flour, baking powder, and fine salt. Add the dry ingredients to the butter mixture and mix just until a soft dough forms.

Set aside approximately 1 1/2 cups of dough for the crumble topping. Press the remaining dough evenly into the parchment-lined pan.

Toss the diced strawberries with the sugar, cornstarch, and lemon juice. Spread the strawberry preserves over the cookie base, then distribute the fresh strawberry mixture evenly over the preserves.

Break the reserved dough into uneven pieces and scatter it over the strawberries. Leave a few small areas of the fruit filling visible rather than covering the surface completely.

Bake for 35–40 minutes, until the topping is lightly golden and the filling is bubbling around the edges. Cool the bars completely in the pan before slicing.

For cleaner cuts, refrigerate the cooled bars for 30 minutes. If desired, whisk the powdered sugar with 1–2 tablespoons of milk or lemon juice and drizzle it over the bars before serving.