If using fresh corn, grill or roast the corn on the cob until lightly charred, then cut the kernels off. For frozen corn, thaw and pat dry.
In a large skillet over medium heat, add corn kernels and cook for 5-7 minutes, stirring occasionally, until corn is slightly browned and smoky.
In a large bowl, combine the crema, mayonnaise, lime juice, smoked paprika, chili powder, cumin, garlic, and jalapeño. Stir well to combine.
Add the cooked corn, Cotija cheese, mozzarella (or Monterey Jack), cilantro, salt, and pepper. Mix until evenly combined.
Transfer the dip to a serving bowl and garnish with additional Cotija cheese, cilantro, and a sprinkle of smoked paprika if desired.
Serve warm or at room temperature with tortilla chips, sliced bell peppers, or cucumber rounds.