Place a well seasoned cast iron skillet on the center rack and turn oven on to preheat at 425F (218C). If your skillet is not well seasoned, use a dutch oven or oven proof skillet that has a lid (see notes). Meanwhile, wash the outside of the artichoke, gently nudging the leaves open a bit to wash out any loose dirt. Pat dry.
Remove leaves at the base of the stem until a bit of white is showing at the base of the artichoke. Use a vegetable peeler to peel off the tough outer layer of the stem, starting at the base to about 1" down the stem. Cut the stem with a serrated knife to about 1". Rub with a lemon to prevent oxidation. If the leaves are particularly prickly, trim the tips of the leaves, but I find, most of the time, this is an unnecessary step. So forge ahead without if you wish. Use a serrated knife to slice the artichoke in 1/2, from stem to tip. Take 1/2 a lemon and squeeze, generously, lemon juice all over the exposed areas of the artichoke. Using a pastry brush, bush olive oil all over the artichokes, both on the exposed inside and outside, getting into the cracks and crevices.
Carefully remove the skillet from the oven and place the artichokes cut side up on the skillet. Sprinkle with sea salt. Place a few slices of lemon in the pan and place the pan back in the oven to roast. Set a timer for 20 minutes.
After 20 minutes of roasting, pull the pan from the oven. Using a pair of tongs, turn the artichokes over, face down and pour 3 Tbs of water into the pan. It will steam and sputter, so be careful here. Quickly cover the pan with a lid and place the pan back in the oven for 25 minutes. Test to see if artichokes are done by forking the base of the choke for tenderness. If needed, give the artichokes 5-10 more minutes, covered, adding a few more Tbs of water for steam. The time can vary depending on the size of the artichoke.
Remove from the oven and allow to cool enough to handle. Remove the choke (the fuzzy purple part) of the artichoke using a spoon. Scoop from the bottom of the choke and out, removing the purple leaves and the fuzzy hairy parts. Be sure not to scrape the bottom of the artichoke, because this is the sublime part, the heart, to enjoy after the leaves have been picked through.
Sprinkle again with a bit of salt, and fresh ground pepper. Serve with wedges of lemon warm or at room temperature.