01 - In a small mixing bowl, whisk together the olive oil, balsamic vinegar, soy sauce, minced garlic, chopped rosemary, smoked paprika, black pepper, and salt until well combined.
02 - Place the Portobello mushroom caps gill-side up in a large baking dish or resealable bag. Pour the marinade evenly over the mushrooms and let them soak for at least 15 minutes, or up to 2 hours for deeper flavor, turning halfway through.
03 - Preheat an outdoor grill or grill pan over medium-high heat. Remove the mushrooms from the marinade, reserving any excess for basting.
04 - Place the mushrooms cap-side down on the hot grill. Cook for 5 to 6 minutes per side, basting occasionally with the reserved marinade, until tender and deeply browned.
05 - Serve hot as a main course, or slice and layer into sandwiches or toss over salads.