01 - In a small 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 a resealable plastic bag. Pour the marinade evenly over the mushrooms and let them soak for at least 15 minutes, or up to 2 hours for a more intense flavor, turning them halfway through.
03 - Preheat an outdoor grill or grill pan over medium-high heat. Remove the mushrooms from the marinade, reserving any leftover liquid 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 the mushrooms are tender and deeply browned.
05 - Serve the Portobello steaks hot as a main course, or slice them and layer into sandwiches or toss over salads.