Preheat oven to 350°. Butter an 8-inch square-baking pan. Line bottom with parchment paper, leaving an overhang on two sides; butter and flour paper, tapping out excess.
In a medium bowl, whisk together melted butter, brown sugar, and 1/4 teaspoon salt; add 1 cup flour, and mix with a fork until large moist crumbs form. Refrigerate topping until ready to use.
In a medium bowl, whisk together remaining 3/4 cup flour, baking powder, and remaining 1/4 teaspoon salt; set aside.
In a large bowl, using an electric mixer, beat room-temperature butter, confectioners' sugar, and vanilla until light and fluffy, add eggs, one at a time, beating well after each addition. Reduce speed to low; mix in flour mixture. Spread batter evenly in pan; sprinkle with blackberries, then chilled topping.
Bake until golden and a toothpick inserted in center comes out with moist crumbs attached, 40 to 45. Cool completely in pan. Using paper overhang, lift cake onto a work surface and cut into 16 squares.
Adapted lightly from Martha Stewart
Photo: Smitten Kitchen