Prepare grill for medium-high heat. Brush corn with a total of 1 Tbsp. oil; season with salt and sprinkle with chili powder. Grill, turning occasionally, until tender and lightly charred in spots, 6-8 minutes. Transfer to a cutting board and let cool, then cut kernels from cobs.
Meanwhile, toast coriander and cumin seeds in a dry small skillet over medium heat, tossing, until fragrant, about 3 minutes. Let cool, then chop with a knife or coarsely grind in a spice mill. Whisk with lemon juice, rosemary, hot sauce, and remaining ¼ cup oil in a medium bowl; season with salt and pepper. Add corn kernels, nectarines, onions, basil and cheese and toss to combine. Serve over a bed of chopped lettuce.