Shred potatoes, using coarse shredder blade of food processor. Transfer half the potatoes to a mesh sieve set over a medium bowl.
Change food processor to steel chopping blade. Add onions to potatoes and process until coarsely chopped (about 1/8" chunks), 5-6 one-second pulses.
Move potato-onion mixture to sieve and combine with shredded potato. Squeeze fistfuls of this mixture to remove as much liquid as possible; transfer to a dry bowl. Let remaining liquid sit in bowl until starch settles to bottom, then drain off the clear liquid, leaving the starch behind.
Beat eggs, salt and pepper into starch, then add dry potato-onion mixture and fold together thoroughly. Add matzo meal until mixture is stiff enough to form patties.
Pour oil into 12" saute pan until it is 1/4" deep and heat over medium-high heat until shimmering but not smoking. Take 1/4 cup of potato mixture, press into 1/2"-thick disc and place in oil; press gently with spatula. Repeat until there are 5 latkes in pan.
Adjust heat to keep edges of pancakes bubbling; fry until golden brown, about 3 minutes. Turn over and fry until golden brown all over, about 3 minutes more. Transfer to a triple layer of paper towels on a sheet pan. When oil is shimmering again, repeat. After every two batches, discard the oil and start over with fresh oil; continue this cycle until all the latkes are cooked.
Serve hot with sour cream or applesauce. Latkes may be cooled to room temperature and held up to four hours; to reheat place on a hot cookie sheet in a 375F oven for about 10 minutes, turning once, until hot and crisp. To freeze, place in a single layer on a cookie sheet and freeze until solid, then transfer to a zip-top freezer bag; reheat in a 375F oven until hot and crisp, about 8-10 minutes per side.