Cut the stem from the bottom of the artichokes so it can sit upright, then trim off the tops of the pointy leaves with kitchen shears to make the tops straight across instead of pointy. Fill a large pot with water and bring to a boil. Place the artichokes bottom side down in the pot. If they keep turning over, place a plate on top to help keep them just below the water. Boil for 15 minutes. Once finished, using tongs, carefully remove artichokes from the pot, and let them drain upside down on a large plate or platter.