Remove lamb from refrigerator and set aside – room temperature – for 10 minutes. Preheat gas grill to high and also preheat oven to 350°. In a small bowl, use a wisk to blend the thyme and garlic, adding in the extra virgin olive oil. Rub mixture generously on lamb; season with salt and pepper, to taste, and let sit for 15 minutes.
Slice eggplant, zucchini and tomatoes into ¼ inch medallions. ‘Shingle’ the vegetables – alternating the eggplant, zucchini and tomatoes in a baking dish – and drizzle with extra virgin olive oil. Season with salt and pepper, to taste.
Grill lamb on each side for 3 minutes for medium rare. When the last side of the lamb is grilling, place the ratatouille in the preheated 350° oven for 15 minutes. Remove the lamb from the grill and let rest for 10 minutes while ratatouille is baking.
Spoon ratatouille onto plate and sprinkle with chopped basil. Place 2 lamb t-bones at an angle, partially covering the vegetables. Garnish with a sprig of thyme and serve.