Heat a grill to medium low. Cut the artichokes in half lengthwise and squeeze the juice of half a lemon over the four halves to prevent browning.

Run a pairing knife along the top of the heart just below the fibers. Grab the purple leaves and pull them out, trying to pull out the fibers. Use a spoon to fully clean it.

Rinse the artichoke to clean off all the loose fibers and squeeze the juice of the other half of the lemon over all four halves.

Add ½ cup water to a 13 x 9 microwave-proof dish. Place the artichokes in the dish cut side down. Cover with plastic wrap and microwave for 7 minutes. Carefully remove from the microwave and remove the plastic wrap. The dish and steam will be very hot.

Place the artichokes cut side up and drizzle with olive oil.

Place cut side down on the grill. Close the grill and cook for 6 minutes.

In a small bowl, combine the melted butter, juice of 1 lemon and salt. Flip the artichokes and brush each twice with the lemon butter mixture. Pour the remaining lemon butter evenly into the cavities of each artichoke.

Close the lid and cook for 5 more minutes.

Remove from heat and serve.