How to Make It
Preheat oven to 250°F.
Combine grated potatoes, carrots, and onion in a colander; drain 15 minutes, pressing mixture occasionally with a spoon to extract liquid. Place potato mixture in a clean kitchen towel; squeeze out excess liquid. Place potato mixture in a bowl.
Weigh or lightly spoon flour into a dry measuring cup; level with a knife. Add cilantro, flour, salt, curry powder, garam masala, and crushed red pepper to potato mixture, stirring to combine. Stir egg and egg white into potato mixture.
Heat a large skillet over medium-high. Add 5 teaspoons oil; swirl to coat. Spoon potato mixture loosely into a 1/4-cup dry measuring cup, filling about two-thirds full. Add mixture to pan, and flatten slightly. Repeat procedure 4 times to form 5 latkes. Cook 3 to 4 minutes on each side or until golden brown. Place latkes on a baking sheet; keep warm in oven at 250°F. Repeat procedure twice with remaining 10 teaspoons oil and remaining potato mixture, adding an extra latke to the pan during the last batch to yield 16 latkes total.
Combine yogurt with cucumber; serve with latkes.