Soak garbanzo beans in water for 8 hours to overnight. Drain and rinse beans and transfer to a pot. Add vegetable broth and bring to a boil, about 5 minutes. Reduce heat and simmer for 1 hour. Drain and set beans aside.
Place sweet potatoes and russet potatoes into a large pot and cover with salted water; bring to a boil. Reduce heat to medium-low and simmer for 10 minutes. Drain and set aside.
Meanwhile, add tomatoes to a blender and process until pureed.
Combine curry powder, cumin, garam masala, salt, and cayenne pepper in a small bowl, mixing well and adjusting spices as needed.
Melt ghee in a large nonstick pan over medium-high heat. Add onion and cook until very browned with minimal stirring, about 10 minutes. Add bell pepper, garlic, and ginger and cook while stirring for 2 minutes more. Add spice mixture and cook, string constantly, until very fragrant, 2 more minutes.
Add drained garbanzo beans, cooked sweet and russet potatoes, pureed tomatoes, and coconut milk to the onion mixture in the pan. Stir well and bring to a simmer, about 5 minutes. Cook until heated through, about 10 more minutes.
