Trim the artichokes (see this post for instructions) one by one, immersing them in acidulated water as you go to prevent them from discoloring. Peel the potatoes and immerse them in water as well.

Cut the artichokes and potatoes into thin wedges and add them to a wide skillet with a generous pour of olive oil. Season generously with salt and pepper. Toss the artichoke and potato wedges around so they absorb a bit of the olive oil, then add a glassful of water and cover the skillet. Braise the vegetables until they have softened but retain some 'bite'. Uncover and let any remaining liquid evaporate. Add the chopped garlic (or shallot) and sauté very briefly. Taste and adjust for seasoning—the mixture should be very savory.

In a greased baking dish large enough to hold all your fish, scatter some of the potato and artichoke wedges around the bottom. Season the fish inside and out, then lay them in the dish, covering them with the remaining potato and artichokes wedges. Drizzle everything with some white wine and then a bit more olive oil.

Place in a pre-heated hot oven (200°C/400°F) (use convection heat if you have that feature) and roast until the fish is done, about 15-20 minutes, depending on the thickness of the fish. Let the dish cool for a few minutes and serve immediately, right from the baking dish.