Cut the corn cobs in half crosswise, put them in a large bowl, and toss with the olive oil, 1/2 tsp. kosher salt, and 1/4 tsp. pepper.
Heat a grill to medium-high. Grill the corn until the tips of the kernels are nicely browned all around, about 2 min. on each of three sides. Return the corn to the bowl with the olive oil and toss again. When the ears are cool enough to handle, place the flat end of a cob on a cutting board so the cob is upright and slice the kernels off with a sharp knife. You should have about 1 cup kernels. Set aside until ready to assemble.
Slice the tomatoes 1/2 inch thick and generously season each slice with salt and pepper. On serving plates, arrange one, two, or three slices of tomato per person, depending on how big the tomatoes are. Scatter the corn over the tomato slices. Drizzle basil oil generously over each serving. Garnish with fresh purple leaves, if using.
Serve with grilled bread, which could be brushed with basil oil before grilling.
nutrition information (per serving):
based on eight servings;
Photo: Scott Phillips