Place olive oil, balsamic vinegar, cane syrup, salt, pepper, cayenne pepper, dried basil, dried thyme, dried oregano, and sun-dried tomatoes in a large bowl; stir to combine. Set aside.
Heat a large skillet over medium heat. Working in batches, add about one-third of the marinade to the skillet. Add 4 to 6 oysters to the skillet; cook until oysters begin to curl slightly at the edges and are just cooked through, 1 to 2 minutes. Remove oysters to reserved shell, and top with marinade. Repeat with remaining oysters.
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