Dissolve the salt in one gallon of cold water. Remove and reserve the necks and wing tips. Put the chickens into a small plastic bucket or a large food storage bag (you'll need two gallon-size). Cover with the salt brine solution. Squeeze the air out if using bags. Refrigerate eight hours or overnight. Dump the brine, and rinse the chickens thoroughly to remove all trace of the salt water.
Preheat the oven to 400 degrees. Pat the chickens dry with paper towels. Stuff the cavities with the artichoke hearts, rosemary, and onion.
Put the chickens breast-side down on a roasting pan with a rack. Put the pan into the center of the oven. Lower the temperature to 350 degrees. Do not use the convection feature.
Put the chicken necks, wing tips, and the peppercorns into a small saucepan with just enough water to cover. Bring to the lightest simmer and cook, uncovered, while the chicken is in the oven. Strain and hold. (Or skip this step if you have a cup of chicken or turkey stock around.)
About 45 minutes into the roasting of the chickens, heat the vegetable oil to 375 degrees. Fry the potatoes until medium brown around the edges. Remove and drain. Try not to eat more than five or six of them.
When the chicken is 165 degrees in the breast or 175 degrees in the thighs (temperature taken with a meat thermometer, not touching bone), remove it from the oven and place on a cutting board. Let it cool while you work on the garnish.
Heat the butter in a skillet over medium heat until it bubbles. Add the garlic and mushrooms. Cook until the garlic is fragrant, then add the white wine. Bring it to a boil and cook until most of the liquid has been absorbed. Then add 1/2 cup of chicken stock, salt, and pepper, and reduce to a simmer.
Remove the artichokes from the chicken cavities, and add them to the pan. (It's okay if some of the onions and rosemary get in there, but not much.) Add the peas, green onions and potatoes. Reduce the liquids until the mixture is quite wet but not sloshy.
Cut the chickens into halves, removing the rib bones and backbone. Place on a warm plate and spoon the pan contents over the chicken. Serve immediately.
