Fill a large bowl with ice water.
If using fresh artichokes, prepare as follows:.
- To prepare artichoke bottoms, slice off the stems of the artichokes and remove any tough outer leaves. Place them in a large non-aluminum pot and cover them with cold water. Squeeze the lemons into the pot, add the juice and the lemon halves to the pot, and bring to a boil over high heat. Reduce the heat to a medium and cook until the artichokes are tender, about 25 minutes. Use the tines of a fork to check for tenderness.
Place the artichokes in the ice water. When they are cool enough to handle, drain and remove the leaves and the fuzzy chokes. Trim off the edges of the bottoms.
Preheat the oven to 350 degrees.
Place the artichoke bottoms, eggs, and water in a blender or a food processor fitted with a steel blade and blend until creamy. Pour into a mixing bowl, add the flour, salt, and pepper, and combine until the mixture forms a thick paste.
Whip the egg whites in a dry copper or stainless steel bowl until they hold stiff peaks. Gently fold into the artichoke mixture.
Place a cast-iron skillet over medium-high heat and when it is hot, add the oil. Drop dollops of batter (about 2 tablespoons per pancake), a few at a time, into the hot oil. When the edges begin to stiffen, turn the pancakes over and cook until lightly golden, abut 2 minutes. Place the pancakes on an oven proof plate.
Combine the goat cheese and sour cream in a small mixing bowl. Top each pancake with a large dollop of the goat cheese mixture and place in the oven until the cheese just begins to melt, about 2 minutes.