1. In a large pot of boiling salted water, cook the corn just until tender, about 3 minutes. Drain and cool under running water. Pat the corn dry and, working over a bowl, cut the kernels from the cobs.
2. Heat a large cast-iron skillet or griddle until very hot and brush lightly with oil. In a bowl, toss the okra with 2 tablespoons of the vegetable oil and season with salt. Cook the okra in batches over high heat, turning once, until charred and tender, 3 minutes per batch. Transfer the okra to a platter.
3. Add the remaining 2 tablespoons of oil to the corn kernels, season with salt and toss to coat. Add the corn to the skillet and cook over high heat, stirring occasionally, until lightly charred in spots, about 3 minutes. Add the corn to the okra and toss. Serve hot or at room temperature.