Cut veggies into bite-sized chunks. (Leave mushrooms whole, but trim stems.) Combine veggies, olive oil, balsamic vinegar, bottled minced garlic, honey, pepper, and salt in a large zip top plastic bag. Refrigerate 1 hour or overnight.
Preheat grill to medium heat. Cook pasta according to package directions. Drain.
Add veggies to grill basket. Grill 10 minutes. Stir in tuna cubes. Cook 10 more minutes or until tuna is cooked through. Combine tuna, veggies, and pasta and serve warm.