How to Make It
Preheat oven to 325°F. Grease and flour a 12-inch round tart pan with removable bottom; place tart pan on a rimmed baking sheet lined with parchment paper. Melt butter in a saucepan over medium-high, and cook, stirring often, until butter releases a nutty aroma and milk solids are golden brown, about 8 minutes. Immediately transfer butter to a bowl; cool slightly, about 10 minutes.
Beat egg whites with a heavy-duty electric stand mixer on medium speed until frothy, about 30 seconds. Gradually add powdered sugar; beat until light and fluffy. Gradually add almond flour and 1 cup of the all-purpose flour; beat on medium-low speed until incorporated. Add vanilla bean paste and browned butter; beat on medium-low speed until incorporated. Spread batter in prepared pan. Toss blackberries with remaining 1 tablespoon all-purpose flour, and sprinkle over batter.
Bake in preheated oven until golden brown and a wooden pick inserted in center comes out clean, 42 to 45 minutes. Cool in pan on a wire rack 15 minutes. Remove sides of pan, and cool 30 more minutes. Dust with powdered sugar before serving.