Boil a large pot of water.  

While the water is boiling, cut the artichokes in half. You want to cut it longways, including cutting through the stem (see picture). Take a spoon and scrape out the fuzzy inside. Make sure to leave as many leaves intact as possible. 

Once water is boiling, add artichokes to pot and cook for about 15 minutes, turning over once halfway through cook time.  

While the artichokes are finishing, heat up an outdoor or indoor grill. You can also use a grill pan but make sure to get it very hot.  

Remove artichokes from water and place them on a plate.  Drizzle the cut side of the artichokes with a little olive oil and place them cut side down on hot grill/pan.   

While they are grilling, mix together one cup of mayonnaise with a large spoonful of Old Bay seasoning. Add a good squeeze of lemon juice to the sauce and stir.  

Check the artichokes and see if the leaves are browning and crisping. Once you get a nice grilled look to them, you can remove them from the heat.  

Add a quick drizzle of olive oil, a squeeze of lemon juice, and a good sprinkle of sea salt. Dip leaves into sauce and enjoy!