In a large pot or Dutch oven, heat the vegetable oil over medium heat. Add the chopped onion and sauté until translucent, about 5 minutes.
Stir in the minced garlic and grated ginger, cooking for another 1-2 minutes until fragrant.
Add the ground cumin, coriander, turmeric, and cayenne pepper. Cook for 1 minute, stirring constantly to toast the spices.
Add the chicken pieces to the pot, browning them on all sides for about 5-7 minutes.
Pour in the coconut milk, chicken broth, and tomato paste. Stir well to combine, then bring the mixture to a simmer.
Reduce the heat to low, cover the pot, and let it simmer for 30-40 minutes, or until the chicken is cooked through and tender.
Stir in the lime juice and season with salt and pepper to taste.
Serve the curry hot, garnished with fresh cilantro, alongside cooked rice or flatbread.