Preheat oven to 375°. Combine first 4 ingredients (through vinegar) in a small bowl; set aside.
Place the vegetables (eggplant through red onion) in an even layer on a large baking pan. Brush vegetables on both sides with marinade; sprinkle with sea salt, then place on prepared grill.
Grill for 5–7 minutes or until lightly browned, brushing with marinade, as needed. Turn vegetables occasionally to brown all sides; when cooked, remove from heat and cut into bite-size pieces. Set aside.
Place bread slices on a baking pan lined with parchment paper. Lightly coat with cooking spray. Bake for 4–6 minutes or until lightly browned. Remove from oven, and rub bread with garlic cloves. Set aside.
Combine cheeses, parsley, cayenne, and mustard in a medium bowl. Sprinkle cheese mixture evenly over toast. Return toast to oven, and bake for 5 minutes more or until cheese is browned and bubbly.
Divide greens among 4 plates. Top with grilled vegetables, and serve with 1 Gruyère toast.
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