Shredded carrots lend a subtle sweetness to these otherwise classic potato pancakes. While they're delicious on their own, we've upped the ante with tangy labne and spicy jalapeno relish.
In a small bowl, stir together potato starch, baking powder, 1 1/2 teaspoons salt, and 1/2 teaspoon pepper; set aside. Peel potatoes; place in a bowl of cold water. On the large holes of a box grater, grate potatoes, onion, and carrots. Transfer to a fine sieve lined with cheesecloth and set over a large bowl.
Gather mixture in cheesecloth and squeeze moisture out into bowl. Let stand until a white paste settles to bottom of bowl, about 2 minutes. Remove sieve; pour liquid out of bowl and discard, leaving behind white paste.
Add potato mixture to bowl and sprinkle with baking-powder mixture; toss to coat. Add eggs; stir to combine.
Heat 1/4 inch oil in a large, heavy skillet (preferably cast iron) over medium-high until hot but not smoking. (Test with a shred of potato; if it sizzles immediately, it's ready). Reduce heat to medium. Working in batches to avoid crowding, scoop a scant 1/4 cup of potato mixture into oil; flatten with a spatula to 1/4 inch thick. Fry, turning once, until golden brown and crisp, 3 to 4 minutes per side. Using a slotted spatula, transfer to paper towels set over a baking sheet. Sprinkle with flaky salt. Repeat, stirring potato mixture between batches, and adjusting heat as needed while frying. Serve immediately, topped with labne and jalapeno relish.