Cut each jalapeño in half lengthwise and scoop out the seeds. Place 2 teaspoons of goat cheese in each jalapeño half and top it with a couple of tomato and basil slivers.
Set up the grill for indirect grilling, place a drip pan in the center, and preheat the grill to medium-high.
When ready to cook, brush and oil the grill grate. Arrange the jalapeños