Pour the water into a large soup or stock pot. Add the salt, garlic, bay leaf & olive to the water, bring to a boil, then simmer while you prepare the artichokes.
Prepare the artichokes for cooking by trimming off the stems and the very tip top of the artichoke with a sharp knife. Next, use your cooking scissors...actually, any sharp knife will work if you do not have cooking scissors...& trim off the pointed tip of each leaf. With tongs, place the artichokes in the pot. Slice 1 lemon in half and squeeze over the artichokes, then drop the lemon halves into the pot. With the tongs, roll the artichokes in the water to coat them with the olive oil. Bring the water to a boil for a couple of minutes, then reduce the heat to simmer, cover and cook the artichokes for 2 hours. Keep an eye on the water level and add a little extra water if the level gets too low. Remove the artichokes & cover with aluminum foil. Keep at room temperature until ready to grill.
When ready to grill, cut the artichokes vertically in half, scoop out the choke, douse the artichokes with a little olive oil, and place cut-side-down on the hot grill. Grill for about a minute or so, when you have a nice char, then turn & repeat.
To serve the artichokes, spoon some of Carrie's Skinny Dill Sauce into the center of each half. Be sure to have bowls available for the eaten leaves......voilà!