Using the coarse side of a box grater or a food processor fitted with a medium-coarse grating disk, grate potatoes, parsnips, and shallots. Toss together in a large bowl.
Add eggs, matzo meal, salt, and pepper to potato mixture and toss to mix well.
Pour 3/4 in. oil into a 10- to 12-in. frying pan (with sides at least 2 in. high) over medium-high heat. When oil reaches 350°, scoop 1/3 cup of potato mixture from bowl, then gently turn onto a wide spatula. Press into a patty about 1/3 in. thick, then gently slide pancake into hot oil. Cook 3 or 4 pancakes at a time (do not crowd pan) until edges are crispy and well browned and undersides are golden brown, 2 to 3 minutes. Gently turn and cook until other sides are golden brown, 2 to 3 minutes longer.
Transfer pancakes to paper towels to drain briefly, then keep warm in a 200° oven while you cook remaining pancakes. Serve hot, with Gingered Sour Cream.
Note: Nutritional analysis is per latke.