Pat the shredded chicken dry and season with salt and pepper.
Heat 1 tablespoon vegetable oil in a large pan over medium heat. Fry the chicken without browning for 6–8 minutes until it reaches 74°C / 165°F internally. Remove and set aside.
Peel and dice the onions and garlic. Fry them in the same pan over medium heat, adding more oil if needed. Sprinkle with curry powder and cook for 2–3 minutes. Remove from heat.
Mix the onion and garlic mixture with the yogurt and mango chutney. Add the cooked chicken and let marinate for 15 minutes.
While the chicken marinates, peel and slice the carrots. Wash the sugar snap peas and nectarines, then cut the nectarines into wedges. To soften the sugar snap peas, optionally boil them in salted water for 3 minutes and drain.
Heat the remaining vegetable oil in a large pan over medium heat. Fry the carrots and sugar snap peas for 5–7 minutes until the carrots are tender and peas are firm. Add the nectarine wedges and coconut milk, then simmer for 5 minutes.
Add the marinated chicken with all the sauce. Simmer for 5 minutes. Season with salt and pepper to taste.