Preheat oven to 350°F and line an 8-inch square baking pan with parchment paper.
Cook butter in a heavy saucepan over medium heat, stirring constantly until it foams, turns clear, and then turns a medium brown, about 5 minutes. Add brown butter to a large bowl and whisk in sugar, brown sugar, and vanilla until combined.
Whisk together flour, baking soda, and salt in a medium bowl; add to butter mixture and fold in until incorporated. Reserve ¾ cup of dough for topping (keep chilled); press remaining dough evenly into bottom of prepared pan. Bake crust for 14 to 16 minutes, until lightly golden and set. Transfer to a wire rack and cool for 15 minutes.
Filling:
Combine sugar, salt, and cornstarch in a medium bowl. Add fruit and lemon juice, tossing gently to combine. Spoon mixture over cooled crust and crumble reserved dough over filling.
Bake for another 45 to 50 minutes, or until topping is golden and filling slightly bubbly. Cool completely in pan on a wire rack. Just before cutting, chill in the freezer for 15 minutes. Carefully lift parchment and place bars on a cutting board; cut into squares with a sharp knife.
Glaze:
Whisk together ingredients in a small bowl. Drizzle glaze over bars and let set before serving. Store leftover bars in an airtight container in the refrigerator.