Your Oyster Recipe of the Day: Grilled Oysters with Pico de Gallo. This recipe is not only perfect for Cinco de Mayo, but it’s technique is ideal for first-time oyster cookers. Shawnda at The Brewer & The Baker first grills her oysters, making them easy to shuck. Then she tops with Jack cheese, broils until melted, and tops each with a fresh, simple pico de gallo. Viva las ostras!!!