Heat 3–4 inches of avocado oil in a deep dutch oven or cast iron skillet over medium heat. Bring oil to 350–375°F and maintain this temperature while frying.
In a small bowl, combine ⅓ cup Kewpie mayo and 2 tablespoon black garlic purée. If using whole cloves, mash into the mayo with the back of a spoon. Set aside.
Prepare the artichokes:
Cut off the stem flush at the base.
Slice off the top third of the artichoke.
Peel off all the tough, darker outer leaves until tender yellow ones remain.
Slice each artichoke in half or quarters, depending on size.
Carefully add artichoke pieces to hot oil in batches. Fry until golden and crisp, about 3–5 minutes, depending on size. Do not overcrowd the pan.
Remove fried artichokes to a paper towel-lined plate or tray. Immediately sprinkle with kosher salt while hot.
Serve warm with the black garlic mayo on the side for dipping.