Make the Soprano Sauce: Combine the anchovies, garlic and capers in a small bowl or a food processor. Slowly whisk in the olive oil and season further with salt, if desired. Set aside.
Build a charcoal fire or preheat gas grill.
Make the vegetables: Lightly coat cut vegetables with oil and sprinkle with salt. One by one lay the vegetable slices and green onions on the cooking grate over direct medium heat. (Do this in batches if necessary so the grill is not crowded.) Cook about 5 minutes. Turn the vegetables over. Cook 3 or 4 minutes longer. As soon as vegetables are done, remove from grill and transfer to a platter: the zucchini, radicchio and green onions should be done first; the eggplant will take a little longer and the sweet potatoes will be the last to cook through. While the vegetables are warm, coat with Soprano Sauce. Let cool to room temperature and coat again if necessary.
When all the other vegetables are done, place the tomatoes onto the cooking grate to mark and warm through, about 2 minutes. Coat with Soprano Sauce and place onto the platter with the other vegetables, if desired. Decorate with lemon wedges and serve at room temperature.
Recipe courtesy Elizabeth Karmel, Girls at the Grill