Warm the oil in a large, heavy-based skillet over medium-high heat. Sauté the curry paste and the additional ingredients (if using jar paste) for about 2 minutes until fragrant and slightly dried.
Pour in the chicken broth, stirring to dissolve the paste. Allow it to simmer briskly for 3 minutes until the liquid reduces by half.
Add the coconut milk, kaffir lime leaves, sugar, and fish sauce. Stir to combine, then add the chicken pieces.
Spread the chicken evenly across the skillet. Bring the mixture to a gentle simmer, then lower the heat to medium. Cook for 8–10 minutes, allowing the sauce to thicken and the chicken to cook through.
Taste and adjust seasoning as needed: more fish sauce for saltiness, sugar for sweetness, or even shrimp paste for additional depth.
Stir in the pumpkin and green beans. Cook for another 3 minutes until the pumpkin is tender and the sauce reaches your desired consistency.
Remove the skillet from heat and fold in the Thai basil leaves.
Serve the curry over steamed jasmine rice. Garnish with fresh red chili slices and coriander leaves, if desired.