Preheat the oven to 350°F (175°C). Line an 8-by-8 inch square baking pan with parchment paper, leaving an overhang for easy lifting.

In a medium bowl, whisk together 1 3/4 cups flour, 1/3 cup granulated sugar, 3 tablespoons brown sugar, and a pinch of salt. Mix evenly.

Pour in the 3/4 cup melted butter and add 1 teaspoon vanilla. Stir until a cohesive dough forms. It will be slightly crumbly.

Reserve about one third of the dough for the topping. Press the remaining dough firmly into the bottom of the prepared pan to make an even crust.

Bake the crust for 15 to 20 minutes, until it begins to turn golden at the edges. Remove from the oven and let it cool slightly.

Meanwhile, in a separate bowl, toss 3 cups chopped strawberries with 2 tablespoons granulated sugar and 1 tablespoon flour. Let sit for 5 to 10 minutes so juices start to release.

Spoon the strawberry mixture evenly over the warm crust. Distribute the berries and any juices across the surface.

Crumble the reserved dough over the strawberries in small pieces so you get both crunchy and tender bits.

Return the pan to the oven and bake for 30 to 35 minutes, until the fruit is bubbling and the topping is golden brown.

Remove the bars and allow them to cool completely in the pan on a wire rack.

While cooling, whisk together 1/2 cup powdered sugar, 1 tablespoon cream, and 1/4 teaspoon vanilla until smooth.

Drizzle the glaze over the cooled bars, then lift them from the pan using the parchment overhang.

Cut into 12 bars and serve.