Preheat the oven to 200°F (93°C).
Using the coarse side of a box grater or a food processor fitted with a medium grating disk, grate the potatoes, apples, and shallots. Toss the grated sweet potato, grated apples, and shallots together in a large bowl.
Add the eggs, matzo meal, salt, and pepper and toss to mix well.
Pour 3/4 inch oil into a skillet over medium-high heat. When the temperature reaches 370°F (188°C), scoop 1/4 cup of sweet potato mixture from the bowl and then gently drop the mixture onto a wide spatula. (The point here is to keep your hands as clean as possible.) Press the sweet potato mixture into a patty about 1/4 inch thick, then gently slide the pancake into the hot oil. Cook 3 or 4 pancakes at a time (do not crowd the pan) until the edges are crisp and well browned and the undersides are golden brown, 4 to 5 minutes.
Gently turn the latkes and cook until the other side is golden brown, 2 to 3 minutes longer.
Transfer the pancakes to paper towels to drain briefly, then arrange in a single layer on 2 baking sheets. Keep the latkes warm in the oven while you cook the remaining pancakes. (You can instead cool the latkes to room temperature, then stack them in single layers between sheets of parchment or wax paper, and freeze them in resealable plastic bags. Crisp in a 325°F (163°C) oven for 15 to 20 minutes before serving.)
Serve the latkes hot with sour cream and applesauce on the side.