How to Make It
Combine potato and salt in a bowl; gently massage with your hands until potato mixture is moist and limp. Rinse potato mixture; drain. Place potato mixture in paper towels; squeeze to remove excess liquid. Place potato mixture, shallots, and shrimp in a bowl, stirring to combine. Stir in flours, 1/2 teaspoon fish sauce, pepper, and egg. Divide and shape potato mixture into 8 (3-inch) cakes.
Heat a large nonstick skillet over medium-high. Add 2 tablespoons oil; swirl to coat. Add 4 cakes to pan; cook 2 minutes on each side or until golden brown and crisp. Remove cakes from pan. Repeat procedure with remaining 4 cakes and remaining 2 tablespoons oil. Keep warm.
Combine sugar, 2 tablespoons water, juice, and vinegar in a bowl, stirring with a whisk until sugar dissolves. Stir in remaining 2 teaspoons fish sauce, carrot, garlic, and chile; let stand 15 minutes, or refrigerate up to 3 days.
Serve potato cakes with sauce, lettuce leaves, cilantro, and mint.
The Pho Cookbook.
Ten Speed Press, $22, on sale Feb. 7, 2017.