Heat vegetable oil in a large pot or wok over medium-high heat.
Add jungle curry paste and fry for 2-3 minutes until fragrant and oils begin to separate.
Add chicken pieces and cook for 3-4 minutes until sealed and lightly browned.
Pour in water and add torn kaffir lime leaves. Bring to a boil.
Add butternut squash and simmer for 8-10 minutes until starting to soften.
Add baby corn, green beans, and green peppercorns. Continue simmering for 5-7 minutes until vegetables are tender.
Season with fish sauce and palm sugar, adjusting to taste.
Remove from heat and stir in fresh holy basil leaves.
Serve immediately with steamed jasmine rice.