Ingredients
3/4 cup (1 1/2 sticks) unsalted butter, room temperature, plus more for baking dish
1 3/4 cups plus 1 tablespoon all-purpose flour (spooned and leveled), plus more for baking dish
2 teaspoons baking powder
1/2 teaspoon coarse salt
1 cup packed sweetened shredded coconut
1 cup plus 1 tablespoon sugar
3 large eggs
3/4 cup buttermilk
2 teaspoons finely grated lime zest, plus 2 tablespoons lime juice
3 cups mixed berries, such as raspberries, blackberries, and blueberries (about 1 pound)
3 tablespoons amber rum or orange juice
Preparation
Preheat oven to 350 degrees. Butter and flour a 9-by-13-inch baking dish. In a large bowl, whisk together 1 3/4 cups flour, baking powder, salt, and coconut. In another large bowl, using an electric mixer, beat butter and 1 cup sugar on high, scraping down bowl as needed, until light and fluffy, 4 minutes. Add eggs, one at a time, and beat until combined. With mixer on low, add flour mixture in 3 additions, alternating with 2 additions buttermilk, and beat until combined. Stir in lime zest and juice. Pour batter into dish. Smooth top with a small offset or rubber spatula.
In a medium bowl, toss together 1 tablespoon flour, 1 tablespoon sugar, berries, and rum. Scatter berry mixture over batter. Bake until cake is golden at edges and a toothpick inserted in center comes out clean, about 35 minutes. Let cake cool in pan on a wire rack 20 minutes before slicing. Serve warm or at room temperature.