How to Make It
Preheat oven to 350°F. Melt 1/4 cup butter in a 10-inch cast-iron skillet over medium. Stir in lemon juice, 1/2 cup sugar, and 1/2 teaspoon salt; cook, stirring, until mixture is bubbly and sugar is mostly dissolved, about 2 minutes. Remove skillet from heat.
Toss berries and 2 teaspoons lemon zest in a medium bowl until combined. Arrange berries evenly over sugar mixture in skillet. (If using halved large blackberries, place cut sides up.) Set aside.
Place remaining 1/2 cup butter and remaining 1 cup sugar in bowl of a stand mixer fitted with the paddle attachment. Beat on high speed until mixture is light and fluffy, about 3 to 5 minutes. Reduce speed to medium. Add eggs, 1 at a time, beating well after each addition. Beat in vanilla extract and remaining 2 teaspoons lemon zest.
Whisk together flour, baking powder, baking soda, and remaining 1/2 teaspoon salt in a medium bowl. Add flour mixture one-third at a time to butter mixture alternately with buttermilk, beginning and ending with flour mixture, beating on low speed until just combined after each addition. Spoon batter over berry mixture in skillet, and spread gently over berries.
Place skillet on a rimmed baking sheet. Bake in preheated oven until cake is lightly browned and a wooden pick inserted in center of cake comes out clean, 40 to 45 minutes. Remove from oven, and let cool 30 minutes.
Run a butter knife around edge of cake; place skillet over low to just warm bottom, about 2 minutes. Remove skillet from heat; carefully invert cake onto a large plate. Serve cake lightly dusted with powdered sugar and, if desired, with whipped cream on the side.