In a small mixing bowl, combine softened butter, sriracha, cilantro, salt, green onion, lime juice and zest and mash with the back of a fork until everything is evenly mixed. Set aside.
Preheat barbecue grill to medium-high, approximately 450 F (230 F)
Place oysters directly on grill making sure they aren’t wobbly. Close lid and cook for about 5 minutes, or until edges curl slightly and oyster brine begins to bubble. Top each oyster with a dollop of sriracha-lime butter, close lid and cook for another 2 to 3 minutes.
Using tongs or heat resistant gloves, carefully remove oysters and set onto a serving platter lined with a layer of coarse rock salt, fresh greens or herbs to keep them from tipping over.
Leftover Sriracha-Lime Butter will keep up to 5 days and can be used stirred into a pasta sauce, as a popcorn topping or melted onto fresh corn on the cob.