Pat short ribs with a paper towel to remove moisture and season with salt. For even cooking, let it sit at room temperature for 1 hour.
Meanwhile, cook garlic and ⅓ cup oil over medium-low heat, stirring regularly, until the garlic is barely golden and just starting to crisp, about 4 minutes. Transfer garlic and oil to a bowl; let cool slightly. Stir in parsley and peppers, then season with kosher salt. Let it cool completely.
Heat a cast iron skillet over medium-high heat for 5 minutes. Pat the meat down again and rub it with the remaining 2 tablespoons of oil. Cook meat, turning occasionally, until deeply browned and crusty all over, about 4 minutes for wider sides and 2 minutes for shorter sides. Transfer to a cutting board, loosely cover in aluminum foil, and let rest for 10-15 minutes before slicing against the grain.
Spoon garlic and infused oil over the meat and splash with vinegar; sprinkle with sea salt.