Preheat your grill or broiler until hot, and prepare the corn by husking and cleaning it.
Place the corn on the grill or under the broiler, turning occasionally, until kernels are blistered and charred in spots—about 8 to 10 minutes. You should hear a gentle sizzling and see blackened patches forming.
While the corn is grilling, mix mayonnaise, lime juice, chili powder, paprika, and a pinch of salt in a bowl until smooth and well combined.
Once the corn is evenly charred, carefully remove it from the heat and brush generously with the mayo mixture, allowing the creamy coating to melt into the warm kernels.
Drizzle melted butter over the coated corn for a glossy finish and extra richness.
Sprinkle crumbled Cotija cheese generously over the top, pressing slightly so it adheres to the creamy coating.
Serve the elote immediately while still hot, with extra lime wedges on the side if desired for an extra zing.