Place half of the basil leaves, the sesame oil, lime juice, and slat and pepper in a food processor fitted with a chopping blade and pulse until smooth.
Add the olive oil slowly to bring the mixture to a flowing liquid consistency.
Brush the grill with olive oil using a high heat brush or, alternatively, a paper towel folded in half and rolled into a tube. Place the squash rounds on the hot grill the first side about 2-3 minutes.
Brush the basil mixture on the top of each round, then flip. Brush more of the basil mixture on the second side and continue grilling til fork tender, about another 2-3 minutes.
Drizzle any remaining dressing on a plate and stack the squash rounds on top. Serve warm.