Pour the beans into a large iron skillet, and bring to a boil. Cook at a hard simmer until they become pasty and begin to resemble burrito beans in texture.
Heat oil in a separate skillet over medium heat. Stir in artichoke hearts, onion, and garlic; cook until the artichokes become golden brown.
Place tortillas in a dry skillet over low heat to warm. Remove from skillet. Spoon beans and artichoke mixture onto each tortilla, and top with cheese and tomato. Fold in ends, and roll up.