Heat ¼ cup of olive oil in a large saucepan over medium heat (4 to 5 quarts) until the oil is shimmery. The pan needs to be able to hold all the artichokes in a single layer.
Add the shallots, carrot, garlic, fennel and coriander seeds and cook until shallots are tender, stirring occasionally. This should take about 3 to 4 minutes.
Add the 1 ½ cups of water, lemon zest, and 3 Tablespoons of the lemon juice. Then bring the mixture to a simmer.
Put the artichokes upside down into the shallot mixture so the stems are standing up.
Sprinkle with salt and pepper.
Cover the artichokes with a sheet of wax paper. Place the lid on the pot and simmer for 25 to 30 minutes. The bases should be tender, test them with a knife.
Remove the artichokes from the liquid and let them cool. Let the liquid cool separately.
Once cooled, cut the artichokes in half lengthwise, then scoop out the fuzzy choke and discard. (Make sure any remaining sharp leaves are also removed.)
In a large heavy skillet (I like to use my 12-inch cast iron pan) heat 2 Tablespoons of the olive oil until shimmery.
Place half of the artichokes with the cut sides down in the hot oil and cook until golden brown.
Remove from the oil and repeat with the second half of the artichokes, about 2 minutes per batch.
Place the browned artichoke hearts into your serving dish.
Heat the remaining 2 Tablespoons olive oil in the same skillet over medium-high heat, then add the reserved cooking liquid and 1 Tablespoon of lemon juice.
Bring to a boil and boil for 3 minutes.
Stir in the parsley. Then pour this mixture over the artichokes in the serving dish.
Serve warm or at room temperature.