Heat sunflower oil in a saucepan over medium-high heat. Place chicken pieces skin-side down and fry for 5-7 minutes until the skin is golden brown. Turn pieces over and fry for another 2-3 minutes. Remove from pan and set aside.
Reduce heat to medium. Slice the garlic cloves thinly and roughly chop the onions. Sauté in the same pan with remaining oil for 2-3 minutes until softened.
Cut the carrots into julienne strips approximately 5 mm thick and 4-5 cm long. Sauté for 2 minutes.
Pour in the tomato puree and Thai sweet chili sauce, stirring to deglaze the pan.
Return the chicken to the pan and bring to a simmer. Cover and simmer over low heat for 1 hour, until the chicken reaches an internal temperature of 74°C (165°F).
Roughly chop the parsley and sprinkle over the finished dish. Season to taste.