Rinse and dry or gently wipe off the mushrooms with a damp paper towel. Trim the stem so the mushroom cap can rest flat. With a fork, prick top of mushroom cap several times. In a mixing cup or small bowl, mix the balsamic, 2 tbsp/30ml olive oil, mustard, oregano, coriander, salt, and pepper. Whisk until well blended. Add the mushrooms to a large ziploc bag. Pour in the marinade. Close and move everything around to completely coat the mushrooms. Set in the fridge for 20-30 minutes. Slice the onion into ¼"/6mm quarter circles. Mince the garlic. Heat 2 tbsp/30ml in a large frying pan on medium. Add the onion and garlic. Cook for 12-15 minutes, stirring regularly until golden and fragrant. Line a baking sheet with foil. Turn the oven to broil and place the oven rack in the upper third (but not directly under the heating element). Place the mushrooms cap side up on the baking sheet. Cook for 5 minutes under the broiler. Flip and cook for another 4-5 minutes until barely starting to char. Slice the buns. For best results drizzle a bit of olive oil and toast for a minute or two under the broiler. Assemble the burgers. Place a cooked portabella cap on the bun (or slice the mushrooms) place a small handful of arugula and 1-2 tbsp of caramelized onions on top. Cap with the top bun and serve.