Heat the grill to high, about 450°F. Brush the corn lightly with olive oil.
Grill the corn directly on the grates, turning every 3 minutes, for 10 to 12 minutes total, until you have plenty of blackened, charred spots. Set aside to cool for 10 minutes.
While the corn cools, whisk together the mayonnaise, sour cream, lime juice, chili powder, smoked paprika, and salt in a large bowl.
Stand each cob upright in a wide bowl and slice downward with a sharp knife to cut off the kernels.
Add the warm kernels, red onion, jalapeño if using, and most of the cilantro and cotija to the dressing. Toss well.
Top with the remaining cotija and cilantro. Serve warm or at room temperature.