Whisk together the vinegar, oregano, garlic, salt and pepper in a mixing bowl. While whisking constantly, slowly drizzle in the olive oil. Continue whisking to form an emulsion. Pour the marinade into a shallow container and add the sliced zucchini and Portobello mushroom. Marinate at room temperature, turning occasionally, at least 1 hour or up to 4 hours.
The tomatoes
Prepare the grill for medium-high direct cooking. Place the mushroom cap on the grill, stem side up, and grill for 3 minutes. Place the zucchini slices on the grill and cook for 3 minutes. Flip the zucchini and mushroom over and continue cooking another 3 to 4 minutes. Remove from the grill and cool slightly.
When cooled, roughly dice the mushroom and zucchini. In a mixing bowl, combine the zucchini, mushroom, basil, diced chiles, bread crumbs and 1/4 cup of the grated cheese. Stir to mix. Season with salt and pepper. (Stuffing may be prepared one day ahead and held, covered and refrigerated.)
Slice the tops off of the tomatoes and carefully remove the pulp leaving the shells intact. Spoon the zucchini-mushroom mixture into each tomato and sprinkle with the remaining grated cheese.
Preheat the oven to 350 degrees F. (or prepare the grill for medium-high indirect cooking). Place the tomatoes in a casserole dish and bake for about 20 to 30 minutes or until thoroughly warmed. Transfer to a serving dish, drizzle with olive oil and garnish with fresh basil.
