To make the Garlic and Herb Oil, put all the ingredients into a small saucepan and put it over low heat. Cook for about 5 minutes, just until it becomes aromatic. Set aside and allow the oil to cool.
Bring a large pot of water to a simmer. Squeeze in the juice from 1 lemon and throw the lemon halves in as well. Trim and halve the artichokes and remove the chokes. Put them into the pot and cook them until they are tender, about 10 minutes. Drain and set aside.
Heat the grill to low. Have a large shallow dish filled with 1 cup olive oil. Coat the eggplant, zucchini, peppers, artichokes, scallions, and tomatoes separately with the oil. Grill the vegetables, basting generously with the Garlic and Herb Oil, until tender and soft: about 10 minutes for the eggplant, 8 minutes for the zucchini, 15 minutes for the peppers, 10 minutes for the artichokes, and 5 minutes for the scallions and tomatoes. Arrange them on a large platter and garnish with the olives, cheese, and herbs. Squeeze over the remaining lemon juice and drizzle with a bit of olive oil.