Remove the mushroom stems and brush the caps with a damp towel to remove any dirt. Place the mushrooms in a shallow baking dish.
In a small bowl, mix together the vinegar, oil, soy sauce, sugar, onion powder, garlic powder, and cayenne. Season with a bit of salt and lots of black pepper.
Drizzle the marinade over the mushrooms and use your hands or a pastry brush to coat the mushrooms on both sides. Allow to marinate at room temperature for 10 to 20 minutes.
Preheat the grill over medium-high with the lid on for at least 10 minutes to get the grates really hot. Scrub down with a heavy-duty grill brush to remove any gunk or drippings.
Set a small bowl with a few tablespoons of oil near the grill and oil up a wad of paper towels in the oil. Use a set of tongs to rub the preheated grill grates with the oil-soaked towels. Let the oil smoke for 40 seconds or so, then rub with oil again. Repeat twice.
Remove the portobello caps from the marinade, reserving excess marinade for the end. Add to the grill, cap side down, and weigh them down with a cast iron skillet (this helps expel excess moisture, making them meatier and denser). Grill for 4 minutes, then using oven mitts, remove the skillet. Flip the mushrooms and weigh down again, and grill for another 4 minutes, until deeply golden brown. Take the mushrooms off the grill and brush them with the reserved marinade.Tip: to get crosshatch grill marks, rotate the mushrooms by 45-90º after 2 minutes on each side. To assemble a burger, layer your desired condiments to a bottom bun, top with a grilled mushroom, layer with desired burger toppings, and finish with the top bun.