12 ears of corn, husked
6 tablespoonsolive oil, divided
1 cup thinly sliced red onion
2 large tomatoes, chopped
1 cup(loosely packed) fresh basil leaves, large leaves torn
1/3 cup(or more) fresh lime juice
2 tablespoonschopped fresh thyme
Kosher salt, freshly ground pepper
Build a medium-hot fire in a charcoal grill, or heat a gas grill to high. Rub corn with 1 Tbsp. oil. Grill, turning frequently, until corn is charred and heated through, 10-12 minutes. Remove from grill; when cool enough to handle, cut kernels from cobs and transfer to a large bowl. DO AHEAD: Corn can be made 3 hours ahead. Let stand at room temperature.
Place onion in a strainer and rinse with cold water to mellow its flavor. Drain well. Mix onion, remaining 5 Tbsp. oil, tomatoes, basil, 1/3 cup lime juice, and thyme into corn. Season to taste with salt, pepper, and more lime juice, if desired. DO AHEAD: Salad can be assembled 1 hour ahead. Let stand at room temperature.