Begin by preparing the stuffing. Add the cubed bread, olives, garlic, and oregano to a large bowl. Add 1/2 cup of parsley and 1/2 cup of olive oil. Mix to combine and set aside.
Give the artichokes a good rinse under cold water. Slice off the stems so the artichokes sit upright on a flat surface. Immediately rub a piece of sliced lemon on the area that was cut to avoid it from turning brown.
Next, peel off the outer layers of the artichoke leaves. These are often discoloured and tough and are not good to eat. Peel at least one to two layers of leaves off depending on how the artichoke looks. You want to see soft green leaves.
Using a sharp knife, slice 1-2 centimetres off the top of the artichoke. This will open up the artichoke and make it easier to stuff and will get rid of some of the prickly ends of the leaves. Again, rub this area that was just cut with a slice of lemon to avoid it from turning brown.
To stuff the artichoke, pry the leaves back gently and add the filling between the leaves. You don't have to fill in every leaf, just try and distribute the stuffing evenly throughout the whole artichoke. It's way easier to use your hands than a spoon so get right in there! Once the artichokes are both stuffed, set aside.
Bring a large pot with 2-3 centimetres of water in it to a boil. Add the whole potatoes and the halved lemon that was used to rub the artichokes. Nestle the artichokes on top of the potatoes in a single layer. Cover the pot with a lid and bring to a boil. Once boiling, reduce the heat to medium.
Let the artichokes steam for 30-45 minutes depending on the size of the artichokes. Check the water level halfway through the cooking process. If most of the water has boiled off, add a splash more. You can tell when the artichokes are cooked when you can insert a paring knife easily into the base of the artichoke, the artichokes have turned dark green, and their leaves come off easily when pulled.
Remove the artichokes from the pot using a slotted spoon and place on a serving platter or plate. Drain any remaining water from the pot, leaving the potatoes inside. Add 1/4 cup of chopped parsley and 1/4 cup olive oil to the potatoes. Mix the parsley, olive oil, and potatoes together until the potatoes are fully coated. Scoop out the potatoes and arrange them around the artichokes. Garnish with the remaining 1/4 cup of parsley and 1/4 cup olive oil. Serve right away and enjoy!