Coconut-Lime Berry Cake

1 1/2 sticks unsalted butter, room temperature, plus more for baking dish
1 3/4 C. plus 1 Tbs flour, plus more for baking dish
2 tsp baking powder
1/2 tsp coarse salt
1 C. packed sweetened shredded coconut
1 C. plus 1 Tbs sugar
3 large eggs
3/4 C. buttermilk
2 tsp finely grated lime zest, plus 2 Tbs lime juice
3 C. mixed berries, such as raspberries, blackberries, and blueberries (about 1 pound)
3 Tbs orange juice

1. Preheat oven to 350 degrees. Butter and flour 9x13-inch baking dish. In a large bowl, whisk together 1 3/4 C. flour, baking powder, salt, and coconut.

2. In another large bowl, using an electric mixer, beat butter and 1 C. 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 three additions, alternating with two 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.

3. In a medium bowl, toss together 1 Tbs flour, 1 Tbs sugar, berries, and orange juice. 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. (Refrigerate cooled cake, wrapped tightly in plastic, up to 5 days.)