Prepare the water. Fill a large bowl with cool water, then squeeze the juice from 2 lemons inside. Add the lemon halves directly to the bowl.
Clean the artichokes. Cut about ½-inch off the top of each artichoke, then remove the tougher, outer leaves until you get to the pale-green yellow leaves. Next, use a paring knife to shave off the outer fibrous layer from each stem (this can also be done with a vegetable peeler), as well as cutting off and discarding the bottom ¼-inch. Immediately place cleaned artichokes into the lemon water. Repeat with remaining artichokes. Allow them to soak for 10 minutes before proceeding.
Drain the artichokes, then pat dry well with paper towels to remove excess water.
Heat the oil. Heat oil in a large deep pot over medium heat until it reaches 275F, no higher or they’ll burn. There should be enough oil that the artichokes are fully submerged while cooking, about 3-inches.
Fry the artichokes. Carefully add the artichokes to the hot oil, then cook until they’re tender, but not browned, about 5-10 minutes for smaller artichokes, or up to 15 minutes for larger artichokes. Adjust the heat as needed to maintain the temperature of the oil. Work in batches, if needed.
Press into a flower shape. Use a spider or slotted spoon to carefully remove the artichokes (allowing excess oil to drip back into the pot). Place on a paper towel lined wire rack, then cool for a few minutes until you’re able to handle them. Either use your hands to open up the artichoke leaves so it resembles a flower or very gently press them down gently onto a cutting board. Note: if using larger artichokes, you should use a spoon to scoop out the fuzzy heart at the center and discard.
Fry again. Increase the heat to medium-high and bring the temperature of the oil up to 350F. Once hot and working in batches, carefully add a few of the artichokes at a time to the oil. Make sure there’s a little space between the artichokes so as not to overcrowd the pot. Cook for 30-60 seconds for smaller artichokes, or about 1-2 minutes for larger artichokes, or until they’re a deep golden brown and crispy.
Drain the artichokes. Carefully transfer each fried artichoke to a paper towel lined wire rack then sprinkle with a pinch of Kosher salt while still warm. I like to turn them cut side down (to allow excess oil to drip off) after seasoning. Allow to cool for 5-10 minutes, then enjoy with lemon wedges and/or aioli.