1. Clean the crabs; remove face, gills, and back of each crab (or have your fishmonger do it for you).
2. Whisk together the egg white and milk. Using 2 tablespoons flour, lightly dust each crab on both sides. Season to taste with white pepper. Dip each crab in egg mixture to coat. Combine taro root with the remaining 1 1/2 teaspoons flour. Using about 1/4 cup of the julienned taro root per crab, make a small mound on top of each crab, pressing to adhere. Reseason with white pepper.
3. Heat the vegetable oil in a nonstick skillet over high heat. Reduce heat to medium, and carefully slide the crabs into the skillet, taro-root-side down. Cook for about 2 minutes on each side, adding more oil if necessary.