Heat the oil in a heavy skillet large enough to hold the pieces of Cornish hen in 1 layer. Sprinkle the pieces with salt and pepper. When the oil becomes hot, add the pieces, skin side down. cook over mediumhigh heat until lightly browned, about 5 minutes. Turn and cook 5 minutes more. Add the onions, leeks, and garlic, and cook, stirring, until wilted, about 2 minutes. Add the tomatoes, olives, thyme, wine, chicken broth, bay leaf, saffron, Tabasco, salt and pepper. Stir and scrape the bottom of the skillet to dissolve any brown particles on the bottom. Cover closely, and simmer 10 minutes. Remove the thyme sprigs and bay leaf. If there is too much liquid, reduce the sauce a bit. Sprinkle with basil and serve with mixed vegetables.