Using the medium shredding blade of a food processor, grate the potatoes, laying them horizontally in the feed tube to maximize the strand length. Grate the onions (halve or quarter them first if necessary) on top of the potatoes. The onions will turn to mush, and their juices will help keep the potatoes from turning brown. Pick out any ungrated pieces of potato or onion.
Lay a clean dishtowel inside a large bowl and transfer the grated mixture into the towel. Roll the towel lengthwise and wring out as much liquid as possible (you can do this over the bowl, discarding the liquid, or right over the sink). Depending on the size of the towel (and your muscles), you may have to do this in batches.
Transfer the grated mixture to a mixing bowl. Add the eggs, matzo meal, salt, and pepper; mix well.
In a large cast-iron or nonstick skillet, pour about 1/8 inch of oil and heat on medium high. The oil is hot enough when a piece of potato sizzles when added. Form a trial latke with a tablespoon of the mixture. Fry until golden brown on both sides. Taste and, if needed, add salt and pepper to the potato mixture.
To form the latkes, scoop up about 1/2 cup of the mixture with your hands and loosely pat it into a pancake about 1/2 inch thick, leaving a few straggly strands along the edge. (As you work, liquid will accumulate in the bowl, so lightly squeeze out the excess. The last couple of latkes may need a really firm squeeze.) After shaping each latke, slip it into the hot oil and flatten it gently with the back of a spatula. Fry until deep golden brown, at least 5 min. on each side to be sure the center is fully cooked. If the edges darken very quickly, lower the heat. To prevent excess oil absorption, flip each latke only once. Add oil between batches as needed, making sure the oil heats up again before frying more latkes. Drain the latkes on paper towels or a clean brown paper bag. Serve immediately with applesauce and sour cream.
Latkes are best served right away, but you can reheat leftovers in a 300°F oven. Set the latkes directly on the oven rack (to ensure that air circulates around their entire surface, keeping them crisp) and bake until hot, 8 to 10 min.