Place a broiler pan about 6 inches from the source of heat; preheat the broiler and broiler pan. In a large bowl, whisk together 1 Tb oil, the tea, vinegar, parsley, garlic, mustard, marjoram, salt and pepper; set aside. Trim mushroom stems and reserve for another use. Wipe mushroom caps clean with a damp paper towel. Brush the mushroom caps with the remaining 1 Tb oil and season lightly with salt and pepper.
Place the mushrooms, rounded side facing up, on the preheated broiler pan and broil until tender and lightly browned, 2 to 4 minutes per side. While the mushrooms broil, add salad greens to the dressing and toss. Arrange the greens on 4 individual salad plates. When the mushrooms are done, cut them into thick slices and set them on the greens. Crumble cheese over the mushrooms and scatter tomatoes over all. Add a grinding of black pepper and serve.