There are a number of different ways to cook artichokes, depending on their size, age and of course, local cooking methods.
This is one of my favorite summer pasta dishes using these small purple-ish artichokes. Of course I realize these artichokes aren't available everywhere, even over here the regular supermarkets don't carry them. I have to look in ethnic shops. These are quite small ones compared to the more easier to find french green artichokes that are much larger.
Start by cutting at least 1/3th of the top of the bulb, even then the remaining tops will be a little chewy. Then, using a very sharp knife, peel the outer leaves off or simply tear them off, one by one, then even out with a knife. Also peel the stalk.
Now cut them from top to tail in quarters and remove what we call the "hay" which you probably call the "beard" in the center.
I cut the segments another time from top to tail. You need to plunge these asap in lemony water (squeeze lemon juice in cold water). Artichokes oxydize very quickly, so you need to work quickly. Rubbing them with half a lemon also helps.
For the rest of the recipe I used french Bayonne ham (there's indeed much more than that stereotype Italian ham!), garlic, chili (very mild ones, pips removed), parmezan and a little tomato concassé (peel tomatoes, quarter, cut away pips, cut the remaining flesh in small cubes). I used capellini pasta wich is a very thin spaghetti.
Start by frying the artichokes in a pan for several minutes in olive oil or as I did in butter on medium high heat. When they start to take a little color, add 4 lightly crushed cloves of garlic and finely sliced chili. Let fry for a few minutes, s&p and then add half a cup of water; no stock, no white wine, just water, we want clean flavors. Cover with a sheet of alumium foil or a lid and let braise for at least 45 minutes. You need to test with the tip of a knife if they're done, don't be surprised it takes up to 60 minutes! Meanwhile, cook the pasta in salted water and keep a cup of the hot boiling water.
Now remove the garlic from the artichokes. Away from the heat, add the shredded ham and tomato cubes. Don't add these sooner or the ham will turn out chewy. Taste for seasoning! Add a little cooking water of the pasta if strictly necessary. Add also a teaspoon worth of cold butter. Add the pasta, parmezan or even better, pecorino and parsely. Enjoy!