Preheat grill to high heat for at least 10 minutes.
Mix all garlic butter ingredients in a bowl until fully combined. Taste and adjust seasoning.
Remove husks and silk from all ears of corn.
Brush corn lightly with olive oil. Season with salt and pepper.
Place corn on hot grill. Do not move for 3 to 4 minutes until char marks form.
Turn a quarter turn every 3 to 4 minutes. Grill for 12 to 15 minutes total until charred on all sides.
Remove from grill and place on serving platter.
Apply garlic butter generously while corn is still hot. Brush, spoon, or roll through the butter bowl.
Sprinkle immediately with extra Parmesan while butter is still melting.
Finish with flaky sea salt and fresh parsley.
Serve immediately with lime wedges.