Preheat the oven to 350°F. Line a 9x9-inch baking pan with parchment paper, leaving some overhang for easy removal.
Add the butter to a saucepan over medium heat. Cook, stirring frequently, until the butter becomes golden brown and smells nutty, about 5 to 8 minutes. Transfer to a bowl and allow to cool for 15 to 20 minutes.
While the butter cools, make the filling. Add the strawberries, granulated sugar, brown sugar, lemon juice, vanilla, cornstarch, and salt to a medium saucepan.
Cook over medium heat, stirring occasionally, for 12 to 15 minutes or until the strawberries have broken down and the mixture is thick and jammy.
Remove from the heat and allow the filling to cool slightly while preparing the crumble.
In a large bowl, whisk together the flour, oats, salt, and freeze-dried strawberry powder.
Add the cooled brown butter, brown sugar, granulated sugar, and vanilla. Stir until large crumbs form and the mixture resembles wet sand.
Press about two-thirds of the crumble mixture firmly into the prepared baking pan.
Bake the crust for 15 minutes.
Remove from the oven and spread the strawberry filling evenly over the crust.
Sprinkle the remaining crumble mixture evenly over the strawberry layer. Do not press down.
Return to the oven and bake for 30 to 35 minutes or until the top is lightly golden and the filling is bubbling around the edges.
Allow the bars to cool completely at room temperature.
Refrigerate for at least 2 hours before slicing and serving.