Preheat oven to 450 degrees. Wash tomatoes and pat dry. Slice tomatoes in half, lengthwise and place on a baking sheet (my Sur La Table nonstick half sheet pans are great!) Pour vinegar into a small ramekin and brush vinegar over the tops of the tomatoes. Then, follow suit with the oil. Sprinkle with salt and pepper.
Roast in the oven for 25-30 minutes or until the tomatoes are beginning to caramelize on top. Remove from oven and turn on broiler.
Top the tomatoes with chopped basil and freshly crumbled feta. Return to oven to broil for 3-4 minutes or until cheese slightly begins to brown. Top with additional fresh basil before serving.