Prepare the mushrooms by removing the stems and cleaning the caps with a damp cloth or paper towel.
Place the mushrooms on a rimmed plate and drizzle with olive oil, balsamic vinegar, and tamari. Sprinkle with the garlic powder, paprika, and pinches of salt and pepper. Use your hands to rub the seasonings into the mushrooms, coating them on both sides.
Heat a grill or grill pan to medium heat. Place the mushrooms, gill side up, onto the grill. Cook for 5 to 7 minutes per side, or until the mushrooms are tender and charred.