Preheat the oven to 250°F (130ºC). Line a baking sheet with parchment paper or foil.
On the large holes of a box grater, shred potatoes. Rinse with cool water; drain well. Place potatoes on a clean kitchen towel. Shred carrots and onion and add to potatoes. Gather edges of the towel and twist to squeeze out as much liquid as possible.
In a large bowl, whisk egg and egg white. Whisk in cornstarch, salt and 1 teaspoon cumin. Add potato mixture; toss well to combine.
Heat a large (12- to 14-inch) skillet over medium-high heat. Add 2 tablespoons of oil to the pan and swirl to coat. Pack the potato mixture into a ¼-cup measuring cup. Add mixture to the pan and flatten slightly. Repeat forming 8 latkes. Cook until browned, 3–4 minutes per side. Place latkes on a prepared baking sheet and keep warm in the oven. Repeat the process with remaining 2 tablespoons oil and potato mixture.
In a small bowl, combine yogurt, garlic and remaining ¼ teaspoon cumin. Serve sauce with latkes.
