Zest the lemon and squeeze the juice into a medium mixing bowl with enough water to hold the pared artichokes. Take an artichoke and break off the tough outer leaves one by one until the remaining leaves are pale yellow with only a hint of green. Cut about ¾-inch off the top and pare the stem to a length of ¾-inch or so. Using a potato peeler or a small knife, peel the stem and cut off any remaining stubs of the discarded outer leaves. Cut in half lengthwise and place in the lemon water to prevent oxidization. Repeat with the remaining artichokes. 

Remove the spines from any salt-packed anchovies and soak them in water for 5 mins (this isn't necessary for oil-packed anchovies, which are already filleted). Heat a large cast-iron pan or other heavy bottomed pan over medium heat. Coat with 2 Tbsp of olive oil, add the anchovies, cover if you have a large enough lid (they splatter) and fry for 30 seconds to break-up the anchovies. Thoroughly drain the artichoke halves and add to the pan cut side down, ideally in a single layer. Sprinkle with some salt and pan-fry until the underside is golden brown, 7-8 minutes. Flip the artichokes, add another Tbsp of olive oil to the pan and fry for another 4-5 minutes. Meanwhile, chop the mint leaves. Once the artichokes are browned on the second side, add the lemon zest and chopped mint to the pan and stir. Taste for salt and serve immediately.