Peel the potatoes and slice them as thinly as possible, between 1/16 and 1/8 inch thick (use a mandoline if you have one). Put the sliced potatoes in a large bowl of cold water to keep them from browning.
Cut the fennel in half lengthwise. Slice the halved fennel crosswise as thinly as possible, between 1/16 and 1/8 inch thick. You should have about 4 cups.
In a bowl, combine the breadcrumbs, cheese, parsley, and garlic. Mix well with your hands, making sure the garlic is evenly distributed.
Position a rack in the center of the oven and heat the oven to 400ºF.
Lightly oil the bottom and sides of a 9x13-inch baking dish.
Without draining the potatoes, use your hands to lift out about one-third of the slices and arrange them in the bottom of the baking dish, overlapping them slightly. (The water clinging to them will generate steam as they bake.) Season with 1/2 tsp. of the salt and a couple of grinds of the pepper. Sprinkle the potatoes evenly with 1/4 cup of the breadcrumb mixture. Drizzle with 1 Tbs. of the oil. Top the potatoes with half of the sliced fennel, spreading it evenly. Sprinkle the fennel with 1/2 tsp. salt, 1/4 cup of the breadcrumb mixture, and 1 Tbs. of the oil. Repeat this layering process, ending with a top layer of potatoes. Season the top layer with the remaining 1/2 tsp. salt and some more pepper. Top with the remaining breadcrumb mixture and the final 2 Tbs. oil.
Cover the dish tightly with aluminum foil and bake for 40 minutes (be sure the aluminum foil is sealed tightly all around the baking dish, or there won’t be enough steam to cook the potatoes). Uncover and continue baking until the potatoes are tender when pierced with a fork and the top is golden brown, 25 to 30 minutes longer. Let rest at least 10 minutes before serving. The tortiera is as good warm as it is hot.
Serve the tortiera with roast lamb, pork, or chicken.