Cut chicken into 1-inch pieces and pat dry. Peel pumpkin, remove seeds, and cut into 1-inch cubes. Open coconut milk and scoop 3 tablespoons of the thick cream from the top into a small bowl - this is what you'll fry the curry paste in.

Heat the thick coconut cream and vegetable oil in a large deep skillet over medium heat until it starts to sizzle. Add red curry paste and fry for 2-3 minutes, stirring constantly, until very fragrant and the oil starts to separate - you'll see it glistening around the edges.

Add chicken pieces in a single layer and cook undisturbed for 3 minutes until golden on the bottom. Stir and cook 2 minutes more - the chicken won't be cooked through yet, that's fine.

Pour in remaining coconut milk, chicken broth, fish sauce, and palm sugar. Stir well and add pumpkin cubes. Bring to a gentle boil, then reduce heat to maintain a steady simmer. Cover and cook for 15-18 minutes until pumpkin is tender when pierced with a knife but still holding its shape.

Taste and adjust with more fish sauce for salt or sugar for sweetness. The sauce should coat the back of a spoon. Remove from heat and stir in most of the basil leaves, letting them wilt. Serve over jasmine rice with remaining basil scattered on top and lime wedges alongside.