In a small bowl, stir together the olive oil, soy sauce, apple cider vinegar, brown sugar, oregano, garlic powder, onion powder, smoked paprika, and a little freshly cracked pepper (about 10 cranks of a pepper mill).
Remove the stems from the portobello mushrooms.* Place the mushrooms in a shallow dish, gill sides up. Pour some of the marinade into the gills, then flip the mushrooms and pour the rest over the top. Let the mushrooms marinate for 30 minutes, flipping occasionally.
Heat a grill or grill pan over medium to medium-high heat. Once hot, add the marinated portobello mushrooms and cook for about 7 minutes on each side, or until the mushrooms are soft and have released most of their liquid.
Build your marinated portobello mushroom burgers on a bun with your preferred toppings. I love the classic mix of mayonnaise, sliced tomato, onion rings, and lettuce or spring mix.