The artichoke stems (if on) are edible if peeled, like broccoli. Use kitchen shears to remove the spiny points of the leaves, and maybe the first layer of outer leaves. If it's a globe artichoke, you'll need to separate the centre leaves with your fingers and remove the hairy "choke" (a grapefruit spoon is good for this task, because of the serrated edge). Scrape out the "choke" and give the whole thing a rinse.
Blend the crumbs and cheeze with seasonings and stuff the centre of each artichoke, packing well. Then cram some of the mixture in the spaces of the outer leaves. Set aside.
In a heavy pot, sauté the onion and garlic until transparent. Add peas, wine, and bay leaf. Stand your artichokes in the pot (the peas help them stand up). Slice any stems into chunks and pop them in too. Season with salt, pepper, bay leaf and a touch of dry dill or thyme. Cover and bring to a simmer to steam-cook until done--between 20 minutes and 1/2 an hour.
My MIL always made this a bit oily because she liked sopping the oily "pot licker" up with bread.
There's no classy way to eat an artichoke; you gotta get in there and tear them apart with your fingers and scrape the goodness out of the leaves with your teeth!