Cut off stems of artichokes and set aside. Cut off top of artichoke leaves, creating a flat top. Cut thorns off top of each leaf on artichoke. Gently stretch artichoke from inside to create hole for stuffing. Cut away little purple/white thorny leaves in center. Peel away outer skin of stems so that it is fresh all around. Chop stems into small cubes for stuffing.
In a large bowl drizzle olive oil over bread cubes until they're moist. Add salt and pepper, chopped onion and garlic, sliced olives and chopped stems. Work together with hands. Check olive oil content by squeezing stuffing into a ball in your hand. If it sticks together, there's enough oil, if not, add more. Stuff mixture tightly into center of artichokes -- as tightly as possible.
In a large stove top pot (i.e. Dutch Oven) add water half way up artichokes. Artichokes should be firmly together in pan. Add salt and 1 1/2 cups of extra virgin olive oil to water. Make certain water is high enough but not beyond half way. Bring water to a slow boil in covered pot. Baste leaves around stuffing with broth from the pan every 15 to 20 minutes for approx. 3 hours. When outside leaves are tender they're done. Before removing from pan, baste stuffing one last time, then pack down stuffing with a fork. Serve with a little bit of broth in bottom of bowl.
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