Heat olive oil in a large pot over medium heat. Add onion and cook 5–6 minutes until soft and lightly colored. Add garlic and ginger and cook 2 minutes. Add all spices and stir for 60 seconds until fragrant.
Add diced carrots and stir to coat in the spice base. Cook for 2 minutes. Pour in crushed tomatoes and vegetable broth. Stir to combine and bring to a boil.
Reduce heat to medium-low and simmer uncovered for 10 minutes until carrots start to soften and the tomato base reduces slightly.
Add drained chickpeas and stir through. Simmer for 15 minutes on medium-low, stirring occasionally, until chickpeas have absorbed the spiced broth and carrots are fully tender. Mash a small portion of chickpeas with the back of a spoon to thicken if desired.
Squeeze in lime or lemon juice and stir. Taste and adjust salt, acidity, or heat as needed. Serve over rice or with flatbread. Top with fresh cilantro, a spoonful of yogurt, and a lime wedge.