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Heat olive oil in a large saucepan over medium-high heat. Add carrots, pepper, onions, and about 1/2 teaspoon salt; cook until translucent, about 6 minutes stirring every now and then. Add garlic and galric, tomatoes, and fresh basil then cook for 2-3 more minutes. Add spices and stir until fragrant.
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Add chickpeas and bring to a boil, then lower to a simmer and cook for 15 minutes.
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After simmering, stir in coconut milk and simmer for 5 more minutes. In a small bowl whisk cornstarch with lime juice and 1 tablespoon of water. Add it to the curry along with the coconut sugar and cook until thickened. Season to taste with salt.
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Remove from the heat, sprinkle with chopped fresh basil and serve with basmati or jasmine rice.