Quarter or sixth the cleaned artichoke hearts and rub lemon juice immediately to prevent them from turning black. Peel and wash the potatoes and cut into 2 - 3 cm pieces.
In a large saucepan, preferably a cast iron one, sauté the onions in the olive oil. They should turn golden yellow, but not dark. Add the garlic, sauté briefly and then add the potatoes and artichokes. Then add the chopped parsley, salt and freshly ground pepper and stir everything thoroughly a few times.
Add about 6 tablespoons of water, reduce the heat, put the lid on the saucepan and simmer gently for about 40 - 50 minutes. You can possibly add a few more tablespoons of water if the liquid has already boiled down. When the potatoes and artichokes are soft, season to taste again and, if necessary, season with salt and pepper.