3/4cup1 1/2 sticks unsalted butter, room temperature, plus more for baking dish
1 3/4cupsplus 1 tablespoon all-purpose flour
2teaspoonsbaking powder
1/2teaspooncoarse salt
1cuppacked sweetened shredded coconut
1cupplus 1 tablespoon sugar
3large eggs
3/4cupbuttermilk
2teaspoonsfinely grated lime zest, plus 2 tablespoons lime juice
3cupsmixed berries, such as raspberries, blackberries, and blueberries
3tablespoonsamber rum
Instructions
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; set aside.
In the bowl of a stand mixer fitted with the paddle attachment, beat butter and 1 cup sugar on high, scraping down bowl as needed, until light and fluffy, about 4 minutes. Add eggs, one at a time, and beat until combined. With mixer on low, add flour mixture in three additions, alternating with two additions buttermilk, and beat until combined. Stir in lime zest and juice. Spread batter into prepared dish. Smooth top with a small offset 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.