Heat 1 tablespoon sunflower oil in a large Dutch oven over medium-high heat. Sear the chicken for 5 minutes until browned on all sides, then remove and set aside.
In the same Dutch oven, fry the finely chopped onion over medium heat for 5 minutes until softened. Add the crushed garlic, lemongrass, chilli pepper, and red curry paste, and sauté for 3 minutes.
Return the chicken to the Dutch oven. Add the palm sugar and pour in the broth. Season with salt and pepper to taste.
Reduce heat to low and simmer for 90 minutes, stirring occasionally, until the chicken is tender and reaches an internal temperature of 74 °C (165 °F).