Preheat oven to 350 degrees. Remove crust from bread and tear into 1/2-inch pieces (you should have 4 cups). Spread in a single layer on a rimmed baking sheet; dry in oven, 10 to 15 minutes. Let cool.
Stand artichokes in a saucepan just large enough to hold them. Add water until 3/4 inch up sides of pan; bring to a boil. Reduce to a simmer, cover, and steam until artichokes are tender, 30 to 35 minutes. (Add more water as needed.) Transfer to a plate; let cool, then slice in half lengthwise. Scoop out fuzzy chokes with a spoon; discard.
Preheat oven to 375 degrees. In a bowl, combine bread, oil, cheese, dill, and broth. Season mixture and insides of artichokes with salt and pepper. Divide stuffing among artichokes, mounding tops; drizzle with oil. Place in an oiled baking dish; bake until heated through and tops are golden brown, about 25 minutes. Drizzle with more oil, top with dill sprigs, and serve.