Meanwhile, soak the corn in cold water. Into a large bowl, zest the lime and squeeze 1 tablespoon juice. Stir in the sour cream, chile powder, and a pinch of salt.
Drain the corn and grill, turning occasionally, until charred in spots and tender, about 10 minutes. Transfer to a cutting board. When cool enough to handle, cut into 2-inch lengths.
Transfer the corn to the sour cream mixture and toss to evenly coat. Sprinkle the cheese all over, pressing gently to adhere.