In the bowl of a food processor, combine all ingredients for the chickpea meatballs except for the flour, along with a big pinch of salt and pepper, until a smooth batter forms. The batter should be tacky, but not sticky. If it seems too wet, add 1 tablespoons of flour at a time until it reaches the desired consistency.
Form the batter into 12-16 meatballs. Heat 2 tablespoons of olive oil in a skillet over medium. Sear the meatballs for 10 minutes, turning every couple minutes until each side is browned. Move to a plate.
To the same skillet, add the shallot and saute until soft, about 2-3 minutes. Stir in the garlic, curry powder, cumin, and turmeric. Toast for 5 minutes until very fragrant. Stir in the butter until melted, then the tomato paste.
Pour in the coconut milk, apple cider, and broccoli. Simmer until the sauce thickens and the broccoli softens, about 8-10 minutes. Remove from the heat and stir in the mango chunks and lime juice. Taste and adjust salt and pepper.
Spoon curry over bowls of steamed rice. Serve with extra mango, chopped cilantro or basil, and lime juice, as desired.