In a large pot or Dutch oven, heat the vegetable oil over medium heat.
Add the chopped onions and cook until translucent. Add the garlic and ginger and cook for another minute until fragrant.
Stir in the curry powder, turmeric powder, and chili powder. Cook for 1-2 minutes to toast the spices.
Add the chicken pieces to the pot and cook until they are browned on all sides.
Stir in the chopped tomatoes and cook until they start to break down.
Pour in the coconut milk and chicken or vegetable broth. Bring the mixture to a simmer.
Add the potatoes and carrots. Simmer the curry for 20-30 minutes, or until the vegetables and meat are tender and cooked through.
Season with salt and pepper to taste.
Garnish with fresh cilantro or basil if desired. Serve hot with rice or bread.
Enjoy your meal!