1. Lay the mushrooms on a greased baking sheet, gill sides up. Whisk together the garlic, sherry, 2 tablespoons of the oil and 2 teaspoons of the salt. Pour the mixture over the mushrooms. Marinate for at least 30 minutes or up to 2 hours.
2. Preheat the oven to 400°F. Divide the cheese evenly among the mushroom caps. Roast until the mushrooms are fork-tender and the cheese is melted, 15 to 20 minutes. Reserve any cooking juices in the pan.
3. Meanwhile, heat the remaining 3 tablespoons olive oil in a large skillet over high heat. Add the onions and cook until charred and tender, stirring often, about 10 minutes. Add the spinach and the cooking juices from the mushrooms. Cook until just the spinach is wilted. Season with the remaining ½ teaspoon salt.
4. Place the mushrooms on the buns and top with the spinach and onions.
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