Heat the vegetable oil or ghee in a large pot or skillet over medium heat.
Add the star anise and whole black peppercorns to the hot oil. Toast for 30 seconds until fragrant.
Add the finely diced onion and sauté for 5-7 minutes until softened and golden brown.
Stir in the minced garlic and grated ginger, cooking for 1 additional minute.
Add the curry powder, stirring constantly for 30 seconds to toast the spices and release their oils.
Add the cubed chicken breast to the pot. Cook for 4-5 minutes, stirring occasionally, until the chicken is lightly browned on all sides.
Stir in the cubed potatoes, diced tomatoes (with juices), and chicken broth. Bring the mixture to a simmer.
Reduce the heat to medium-low, cover the pot, and simmer for 15-20 minutes, or until the potatoes are fork-tender and the chicken is cooked through.
Remove the pot from the heat. Carefully remove the star anise if desired.
Garnish with freshly chopped cilantro and serve immediately over warm rice or with naan.