Trim the artichokes and cut them into wedges. Peel the potatoes and cut them, too, into wedges. Ideally, they should be about the same size as the artichoke wedges. Drop the wedges in acidulated water as you work to avoid discoloring.

In a braising pan large enough to hold all the ingredients, sauté the garlic cloves in olive oil until just lightly brown and discard. Drain the artichoke and potato wedges, and add them to the braising pan. Season well with salt and pepper, and sauté for a few minutes until the wedges are just starting to color around the edges.

Add a splash of white wine and let it cook off. Then add a glassful of water and cover the braiser, turning down the heat to the gentlest flame. Let the vegetables braise until they are both perfectly tender, about 15 minutes or so.

A few minutes before the vegetables are done, mix in the chopped parsley. Taste and, if necessary, adjust for seasoning. Drizzle with a bit more olive and serve your Artichokes and Potatoes while they are still hot.