Preheat your grill to medium-high heat, approximately 450°F.
In a small bowl, whisk together the melted ghee, minced garlic, lemon juice, smoked paprika, sea salt, and black pepper.
Carefully shuck the oysters, discarding the top shells and ensuring the oyster meat remains in the bottom shell with its natural juices.
Place the oysters directly onto the grill grates and spoon roughly one teaspoon of the garlic-ghee mixture into each shell.
Top each oyster with a generous sprinkle of grated parmesan cheese.
Close the grill lid and cook for 5 to 6 minutes, or until the oyster edges curl and the cheese becomes bubbly and golden brown.
Remove the oysters from the grill and garnish immediately with freshly chopped parsley.
Serve the oysters hot with a slice of toasted sourdough bread to capture the flavorful garlic butter juices.