For the chutney: Place the mangoes, apple, brown sugar, ginger, and hot pepper in a food processor and pulse until the mixture is chunky and well combined. Transfer to a medium saucepot and bring to a simmer over medium-high heat. Add the vinegar, season to taste with salt and pepper, and continue to simmer until the fruit is tender and the vinegar has mellowed slightly, stirring occasionally to prevent sticking. Remove from the heat and set aside. Serve warm or at room temperature.
For the pie filling: In a large skillet, heat the vegetable oil over medium-high heat. Add the potato, onion, pepper, celery, and garlic and cook until softened, about 6 minutes. Add the cumin, salt, and pepper. Mix well to ensure that all the vegetables are seasoned. Once the potatoes start to brown, add the vegetable broth, bring to a boil then reduce heat to simmer. Once the liquid begins to reduce add the shrimp and cover skillet. Remove the cover once all the liquid has been absorbed, about 25 minutes. Remove from the heat and allow to cool to room temperature.
For the dough: In a large mixing bowl, combine the flour, baking powder, curry powder, and 1/2 teaspoon salt. Slowly add the water until the dough is well formed and soft but not sticky (you may not use all the water). Knead for 2 minutes on a lightly floured surface and then place in a large bowl to rest for at least 15 minutes. Cover the bowl with a moist cloth or flip the bowl over on a clean prep surface and let sit until ready to use.
Heat the oil in a pot to 360 degrees F. Divide the dough into 8 balls. Flatten into 4-inch circles and place a heaping spoonful of mixture in the center, taking care not to overfill. Wet one edge with water, fold over and seal by pinching the edges with fingers or floured fork. Gently add each pie into the hot oil and fry on both sides until golden brown, 3 to 5 minutes. Drain on brown paper or paper towels.
Serve the pies with the apple-mango chutney.
Cook's Note: This savory Caribbean version of a potato empanada is dressed or served with a warm fruit chutney to enhance the flavors and spices in the pie. It is normally served as a first course starter or a mid-day snack. Proper seasoning and cooking of the potatoes is crucial. If those flavors are not well incorporated it will destroy the dish.