Heat the olive oil in a large sauté pan until quite hot. Add the potatoes, onions, and garlic, stirring to coat. Season with salt and pepper and add the thyme sprigs. Cook uncovered, stirring occasionally, until the onions are soft and the potatoes tender and golden, about 30 minutes.
Toss in the olives and pine nuts, stirring to warm them. Check the seasonings, toss in the basil, and serve.