Toss shredded potato, onion, shallots and salt in a medium bowl. Transfer to a sieve set over a large bowl; let drain for about 15 minutes. Squeeze the potato mixture, a handful at a time, over the bowl to release excess moisture (don't oversqueeze--some moisture should remain). Transfer the squeezed potato mixture to another large bowl. Carefully pour off the liquid, leaving a pasty white sediment--potato starch--in the bottom of the bowl. Add the starch to the potato mixture. Stir in egg.

Put matzo pieces in a sealable plastic bag and crush with a rolling pin into coarse crumbs. Sprinkle the crumbs and pepper over the potato mixture and toss to combine. Cover and refrigerate until the matzo is softened, 20 to 30 minutes.

Preheat oven to 425 degrees F . Coat a baking sheet with cooking spray.

Heat 1 tablespoon oil in a large skillet over medium-high heat. Stir the potato mixture. Cook 4 latkes per batch: place 1/4 cup potato mixture in a little of the oil and press with the back of a spatula to flatten into a 3 1/2-inch cake. Cook until crispy and golden, 1 1/2 to 3 minutes per side. Transfer the latkes to the prepared baking sheet. Continue with 2 more batches, using 1 tablespoon oil per batch and reducing the heat as needed to prevent scorching. Transfer the baking sheet to the oven and bake until heated through, about 10 minutes.