If using fresh artichokes, trim them following the instructions found in this post, and cut them into wedges. Keep them immersed in a bowl of water acidulated with a few drops of lemon juice until you are ready to use them, then drain well.

In a sauté pan or braiser large enough to hold all the vegetables, make a soffritto, or flavor base, by gently sautéing the chopped onion, parsley and, if using, pancetta in olive oil until the onion is soft and translucent, taking care that neither onion nor pancetta browns. Season the soffritto well as it cooks.

After the soffritto is done, the vegetables are added to the pan, along with a small glass of water or broth, covering and letting them braise until they are tender. If you are using fresh artichokes, this should take 10-15 minutes; frozen artichokes are already partially cooked and should only take about 5 minutes or so. Fresh peas also take about 10-15 minutes, depending on their actual freshness, while the frozen variety takes only 5 minutes at the most. Here is when I'd add the vegetables according to type:

If using fresh peas and fresh artichokes: Add the peas together with the artichokes and braise until both are tender, about 10-15 minutes.

If using fresh peas and frozen artichokes: Add the peas first, braise for 5 minutes, then add the artichokes and continue braising until both are tender.

If using frozen peas and fresh artichokes: Add the peas when the artichokes are almost tender, after 10 minutes or so.

If using frozen peas and frozen artichokes: Add them both together and braise until tender, about 5 minutes or so.

In any case, add more water or broth if you see things are drying out, and when the peas and artichokes are both tender, uncover the pan and, if there is still a lot of liquid, raise the heat to evaporate it quickly. Taste and adjust for seasoning. The finished dish should have just a bit of 'sauce' clinging to the vegetables.

Serve immediately. The dish can also be made ahead and reheated.