This is a specialty of my mother-in-law's. I've never seen it offered in local Italian restaurants or other homes, but I'm always asked for the recipe when I serve it. It can be served as a great side dish without the eggs as well.
Trim artichoke stems, cut away leaves, and remove the fibrous portion at the center of the artichoke, leaving the heart. Slice the hearts.
Heat olive oil in a skillet over medium heat; cook and stir artichoke slices and garlic until garlic just begins to turn golden, about 5 minutes. Stir in lemon juice, mint, salt, and black pepper; continue to cook until artichoke slices are tender. Spoon a little water into skillet if juices evaporate.
Pour beaten egg into the skillet and scramble gently until egg is set and not runny, 2 or 3 minutes; serve immediately.