Preheat grill for oven/broil - get it nice and hot. Or just use the gas grill outdoors. Place the mushroom caps, smooth side down, in a shallow dish.
In a small bowl, whisk together vinegar, oil, mustard and italian seasonings. Brush over the mushrooms. Let stand at room temperature for several minutes or so. Also, prepare english muffins. A couple of olive oil sprays on bread and sprinkle with garlic pepper.
Spray grill and smooth side of mushroom with olive oil spray. Place mushrooms on the grill smooth side down. Grill for 5 to 7 minutes, then flip and grill 3 to 4 minutes longer.
After 1st flip place english muffins onto grill to toast. Then flip and add cheese until it is melted. Once english muffins & cheese are complete, the mushrooms should be ready.