Cut each artichoke in half lengthwise, remove the hairy choke, and trim 1 inch of bracts (leaves) from the top.
In a bowl, combine the beef, one egg, the allspice, and salt and mix well. Spoon some of the filling into the cavity of each artichoke, packing the filling tightly and making it flush with the cut surface of the artichoke.
Place the remaining egg in a shallow dish and lightly beat it. Place the matzah meal in another shallow dish. Working with 1 artichoke half at a time, dip the cut side first in the egg, then dredge it in the matzah meal, then set the artichoke half aside.
Pour the olive oil in a Dutch oven and set aside. Heat the vegetable oil in a skillet over medium heat. Add as many stuffed artichokes, filling-side down, as will fit without crowding the skillet. Cook until the breading is golden brown, about 2 minutes. Place the artichokes, filling side up, in a single layer in the Dutch oven. Repeat with the remaining stuffed artichokes.