Preheat grill to medium-high heat (400°F).
Remove husks and silk from corn. Rinse and dry.
Cut each ear in half crosswise.
Stand each half upright. Cut through center to split in half.
Cut each half in half again (8 pieces per ear, 32 total).
Brush corn pieces with vegetable oil on all sides.
Mix melted butter, paprika, chili powder, garlic powder, onion powder, cayenne, salt, and pepper.
Place corn on grill flat side down. Grill 3 to 4 minutes without moving.
Corn will curl into rib shape.
Flip. Brush generously with spicy butter.
Grill 3 to 4 minutes until edges are crispy and charred.
Flip again. Brush with more butter. Grill 2 to 3 more minutes.
Remove from grill. Transfer to platter.
Brush with remaining butter.
Garnish with cilantro, lime, cheese, and chili powder.
Serve immediately while hot and crispy.