1. Heat the oil in a large skillet over medium-high heat. Add the garlic, 1/4 tsp. each salt and pepper, and as much spinach as will fit. Cook, tossing and adding more spinach when there is room, until tender, 2-3 minutes.
2. Meanwhile, heat broiler. Place the rolls split-side up on a foil-lined large broilerproof baking sheet. Dividing evenly, top with the ham, tomatoes, mozzarella, oregano, and 1/4 teaspoon each salt and pepper. Broil until the cheese is melted, 2-3 minutes. Serve with the spinach.
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