Peel potatoes and cut in 8 wedges unless the potatoes are very large or very small.
Brown the potatoes in the three tablespoons of extra-virgin olive oil in a large sauté pan over high heat.
When the potatoes are well-browned, reduce the heat to medium. Add half the onions and garlic.
Sauté until the onion is golden.
Season with salt and freshly ground black pepper to taste. Add approximately ½ cup of water. Cover and cook on medium heat until cooked through, adding more water as needed, approximately 25 minutes. There should be no water left when the potatoes are cooked.
Meanwhile, sauté the remaining onions and garlic in the remaining extra-virgin olive oil in a sauté pan.
When the onions are golden, add the artichokes and salt and pepper to taste. Sauté briefly.
Add white wine, cover and braise until barely tender, approximately 10 minutes. The artichokes will cook further with the potatoes so do not over-cook them.
Add artichokes to the pan with the potatoes.
Sauté, uncovered, about 10 minutes longer, to meld flavors. Adjust salt and pepper.