Preheat the grill to medium-high. Brush the corn with 1/4 cup olive oil and season with salt and black pepper. In a large bowl, whisk together the remaining 1/4 cup olive oil, the garlic, paprika, cayenne and 1/4 teaspoon salt; add the shrimp and toss.
Add the shrimp and corn to the grill and cover. Grill the shrimp, turning once, until opaque, 2 to 3 minutes. Grill the corn, turning occasionally, until lightly charred, about 7 minutes.
Spread the mayonnaise on the corn and sprinkle with the parmesan and a little cayenne. Serve immediately with the shrimp and lime wedges.