Preheat the grill to medium-high heat.
Brush the corn lightly with vegetable oil.
Place the corn directly on the grill grates.
Cook for 10 to 12 minutes, turning occasionally, until lightly charred on all sides.
While the corn grills, combine mayonnaise, sour cream, garlic, and lime juice in a small bowl.
Mix until smooth and creamy.
Remove the corn from the grill and allow it to cool slightly.
Brush each ear generously with the sauce mixture.
Sprinkle the corn evenly with crumbled cotija cheese.
Dust with chili powder and smoked paprika.
Garnish with fresh cilantro.
Serve immediately with lime wedges on the side.