Curry paste and canned Thai coconut cream (unsweetened) can be found at Asian markets, in the international food section of larger supermarkets, or online at Amazon.com. If you cannot find coconut cream, buy coconut milk and skim the thick, rich cream off the top, reserving the milk for another use.
Step 1: Halve the jalapeño peppers lengthwise, cutting through the stems. Use a small spoon or knife to remove the seeds and ribs.
Step 2: Heat the oil in a nonstick frying pan over medium heat until it shimmers. Add the ground chicken and break into small pieces with a wooden spoon. Cook until the chicken is no longer pink. Add the scallions, curry paste, fish sauce, and palm sugar. Stir for 2 minutes. Remove from the heat. Let cool.
Step 3: In a small bowl, beat the egg with a whisk or fork. Whisk in the coconut cream. Add to the chicken-curry mixture. Stir in the basil leaves, if using, and the white rice.
Step 4: Fill each jalapeño pepper half with the mixture and arrange in a single layer in a disposable aluminum foil pan. (Alternatively, you can arrange the poppers directly on the grill grate, balancing them between the rungs of the grate.)
Step 5: Set up your grill for indirect grilling and preheat to medium (about 375 degrees F). Roast the poppers until the peppers are no longer bright green and the filling is hot, 20 to 25 minutes. Arrange on a platter. Serve immediately.