In a medium bowl, combine the softened butter, lime juice, lime zest, chili powder, cumin, cayenne pepper, minced garlic, chopped cilantro, and salt. Mix thoroughly until all ingredients are evenly distributed throughout the butter.
Shuck the corn, making sure to remove all the silk strands. Brush each ear lightly with oil and season with a pinch of salt and pepper.
Heat your grill to medium-high (around 375-400°F). If using a charcoal grill, arrange the coals to create direct and indirect cooking zones.
Place the corn directly on the grill grates. Rotate the ears every 2-3 minutes until you achieve light char marks on all sides, about 10-12 minutes total. The kernels should be bright yellow and tender when pierced with a knife.
Transfer the hot grilled corn to a serving platter. While the corn is still hot, slather each ear generously with the chili-lime butter, allowing it to melt into all the crevices between kernels.
Sprinkle with cotija cheese if using, add a final squeeze of fresh lime juice, and garnish with cilantro leaves. Serve immediately while hot, with extra lime wedges on the side.