Cut the chicken in half lengthwise and pound to flatten the thick part so the chicken is of consistent thickness. Place the chicken in a shallow dish. In a small bowl, mix together the egg, 2 teaspoons cornstarch, 1 teaspoon salt, the pepper, and the ginger. Pour the egg mixture over the chicken, turning the chicken to coat all sides. Cover and refrigerate 30 minutes. Remove the chicken from the marinade; reserve the marinade. In a small bowl, mix together 4 teaspoons cornstarch and 4 teaspoons water. Set aside.

To prepare the sauce, in a small saucepan over high heat, add 1 tablespoon oil and the garlic. Cook the garlic until fragrant, 10 to 15 seconds (do not brown). Add the chicken broth, coconut milk, lime juice, sugar, and vinegar and bring to a boil. Stir in the cornstarch mixture. Cook and stir until thickened, about 10 seconds.

Heat all but 2 tablespoons of the vegetable oil, 1 to 1½ inches deep, in a wok to 350°F. (If using a skillet, be sure to use a pan 4 inches deep to prevent splattering.) Mix the reserved marinade, the flour, ¼ cup water, the remaining 2 tablespoons cornstarch, 2 tablespoons vegetable oil, the baking soda, and the remaining ¼ teaspoon salt. One at a time, dip the chicken pieces into the batter to coat all sides. Fry the chicken pieces for about 3 minutes, or until light brown, turning 2 to 3 times. Drain on paper towels.

Increase the oil temperature to 375°F. Fry the chicken pieces again until golden brown, turning once, about 2 minutes. Drain on paper towels. Using a very sharp knife, cut each piece crosswise into ¾-inch pieces. Place in a single layer on a heated platter. Reheat the sauce over high heat and pour over the chicken.

Garnish the edge of the platter with the cherries, if using, and thin slices of lime.