Wash the artichokes by plunging them upside down in a bowl of water.
Cut 1/2-inch off the tops. Cut the stems to about 1 1/2-inches long.
Go around the artichoke and trim the thorny tips off the outer leaves with scissors. (You don’t have to trim, they just present prettier.)
Rub all the cut ends with half of a lemon to keep them from turning brown from oxidation.
Poke the garlic slivers between the leaves, here and there.
Place the trivet basket in the Instant Pot. Place a steamer basket on top and add the artichokes.
Lock the lid in place. Select Manual and adjust to High Pressure. Set the timer for 7 minutes pressure cooking if you plan to roast the artichokes after pressure cooking, 8 minutes if you are just going to cook them and eat.
When the beep sounds, quick release the pressure by pressing Cancel, and twisting the steam handle to Venting position. You should be able to pierce the base of the stem with a fork.
Transfer to a cutting board until cool enough to handle. Cut in half lengthwise.
Carefully cut out the purple-white-ish fuzzy center. (It’s hard to do this without getting some of the inedible fuzz where you don’t want it. Not to worry—quickly rinse the wayward fuzz away under running water. )
Preheat oven to 400°F. Juice the 1 1/2 lemons and mix with the olive oil.
Pour over the artichoke halves, making sure some flows between the leaves. Sprinkle generously with salt and pepper.
Place the cast-iron skillet, in the oven about 5 minutes, until hot. Swirl in 2 teaspoons of oil.
Place the marinating artichoke halves, cut side down, in the hot skillet. Brush with some of the lemon and olive oil so the leaves are shiny.
Cut the third lemon in quarters and nestle each quarter between the halves.
Roast 20 to 25 minutes until the artichokes are nicely browned, the leaves pull off easily, and the meat on the leaves is tender. (Pull one out to check.)