In a large shallow bowl, whisk together the ingredients for marinade. Place the sliced portobello mushrooms in the bowl then toss until evenly coated in the marinade. Set aside for at 30 minutes, tossing every 10 minutes or so.
Meanwhile, prepare the dressing. Whisk everything together in a small bowl or measuring cup then set aside.
Place the chopped romaine in a large bowl then refrigerate while you grill the vegetables (mushrooms to red onion). Coat the vegetables with high heat oil and grill until slightly tender and golden brown.
Cut the grilled vegetables into smaller pieces then serve immediately overtop of romaine with mozzarella and dressing,