Make the New Orleans-Style Grilled Oysters:

Melt 1 Tbsp. butter in a small Saucepan over medium heat. Add garlic and cook, stirring, until fragrant and light golden in color, 1–2 minutes. Add remaining 5 Tbsp. butter, Worcestershire, hot sauce, dried oregano and salt, and stir to combine until butter is melted. Remove from heat. Taste and adjust seasoning; keep warm.

Scrub oysters to remove any sand or grit. Use an Oyster Shucker to pry shells open, keeping cupped side down and retaining as much liquid as possible. Cut muscles connecting oysters to shells. Place, cupped side down, on a Sheet Pan lined with rock salt (to keep from tipping) and keep chilled in fridge until ready to cook.

Prepare a gas or charcoal grill for high heat and preheat a Grill Frying Pan  (if making 6 oysters at a time) or  Grill Griddle (if making 12 oysters at a time). If your grill has a temperature gauge, heat grill to 450–500F, watching carefully to make sure temperature does not get too high.

Spoon about ½ tsp. of garlic-butter over oysters and into shells, then top with Parmesan. Working quickly, transfer oysters to the Grill Frying Pan or Grill Griddle. Close grill lid and cook until oysters are plump, edges curl, and cheese is melted and lightly browned, 3–5 minutes, depending on size. Transfer to a Baking Slab or Sheet Pan lined with rock salt, top oysters with parsley, and serve with lemon wedges, hot sauce, and bread or crackers with extra garlic-butter for dipping.

Make the Bloody Mary-Style Grilled Oysters:

Melt 1 Tbsp. butter in a small Saucepan over medium heat. Add garlic and cook, stirring, until fragrant and light golden in color, 1–2 minutes.  Add tomato paste and cook, stirring, until brick red, about 1 minute. Add vodka, if using, and deglaze Saucepan, scraping bottom. Add remaining 3 Tbsp. butter, hot sauce, Worcestershire, celery seed, salt, and pepper, and stir to combine until butter is melted and sauce is emulsified. Remove from heat. Taste and adjust seasoning; keep warm. 

Scrub oysters to remove any sand or grit. Use an Oyster Shucker to pry shells open, keeping cupped side down and retaining as much liquid as possible. Cut muscles connecting oysters to shells. Place, cupped side down, on a Sheet Pan lined with rock salt (to keep from tipping) and keep chilled in fridge until ready to cook.

Prepare a gas or charcoal grill for high heat and preheat a Grill Frying Pan (if making 6 oysters at a time) or Grill Griddle (if making 12 oysters at a time). If your grill has a temperature gauge, heat grill to 450–500F, watching carefully to make sure temperature does not get too high.

Spoon about ½ tsp. of Bloody Mary butter over oysters and into shells. Working quickly, transfer oysters to the Grill Frying Pan or Grill Griddle. Close grill lid and cook until oysters are plump and edges curl, 3–5 minutes, depending on size. Transfer to a Baking Slab or Sheet Pan lined with rock salt, top oysters with fresh horseradish and celery leaves, and serve with lemon wedges, hot sauce, and bread or crackers with extra bloody mary butter for dipping.