Add the balsamic vinegar, water, salt, and sugar to a small saucepan. Heat over medium heat until the salt and sugar have completely dissolved.
Slice the red onion very thinly with a sharp knife or a mandoline.
Add the sliced onions, dried oregano, black peppercorns, fennel seeds, red pepper flakes, and fresh oregano (if using) to a clean glass jar. Pour the warm vinegar brine on top and close the jar with a lid. Let it come to room temperature.
Place in the refrigerator overnight or at least 20 minutes before serving.
Video
Notes
You can store these pickled onions in the refrigerator in an airtight container for 14 days.