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1
Whisk together vinegar and 2 tablespoons oil in a bowl; season with salt and pepper to taste.
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2
Set aside.
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3
Preheat grill and lightly oil rack.
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4
Thread mushrooms through stem end onto skewers.
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5
Lightly brush mushrooms, onion, and zucchini with the remaining 2 tablespoons oil; season with salt and pepper.
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6
Grill vegetables, turning occasionally, until peppers are crisp-tender and remaining vegetables are just tender and golden brown, about 5 minutes for peppers and onion, 6 minutes for zucchini, and 8 minutes for the mushrooms.
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7
Transfer peppers to a plate and remaining vegetables to a cutting board.
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8
When cool enough to handle, remove mushrooms from skewers and quarter; transfer to a medium bowl.
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9
Cut onion and zucchini into bite-sized pieces.
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10
Transfer 3/4 of the onion (reserving remaining onion) and all of the zucchini to the bowl of mushrooms.
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11
Add the sun-dried tomatoes, mozzarella, and 2 tablespoons pesto to bowl; season with salt and pepper to taste.
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12
Toss to combine.
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13
Spoon the mixture into pepper halves and grill, covered, until the cheese begins to melt, about 3 minutes.
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14
Transfer to serving plates and arrange arugula alongside the stuffed peppers.
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15
Drizzle arugula with remaining dressing and top with reserved onions.
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16
Serve peppers warm with remaining pesto on the side.
