Toss the chicken with 2 teaspoons salt and 1/2 teaspoon pepper. Whisk 1/2 cup cornstarch and 1/4 teaspoon baking powder in a medium bowl. Coat the chicken in the cornstarch mixture, shaking off any excess. Transfer to a rack set on a baking sheet and let sit, uncovered, to set the coating, 30 minutes.
Meanwhile, heat 2 tablespoons vegetable oil in a small saucepan over medium heat. Add the garlic and ginger and cook, stirring, until just softened but not browned, about 2 minutes. Add the soy sauce, brown sugar, honey, rice vinegar, Sriracha and sesame oil; bring to a simmer and cook until slightly thickened, 6 to 8 minutes. Set the sauce aside.
Fill a large Dutch oven or other heavy pot with 2 to 3 inches of vegetable oil. Heat over medium heat until a deep-fry thermometer registers 350 degrees F. Whisk the flour, remaining 1/3 cup cornstarch and 1/4 teaspoon baking powder and 2 pinches of salt in a medium bowl. Add the vodka and 1/3 cup cold water and whisk until the batter is smooth and very thin (about the consistency of half-and-half). If needed, add more water, 1 tablespoon at a time, to thin the batter.
One at a time, dip about half the chicken pieces in the batter, letting any excess drip off. Then, using tongs, hold the chicken halfway in the hot oil for 1 to 2 seconds before letting go completely (this will prevent the chicken from sticking to the bottom of the pot). If any pieces stick together, gently separate them with the tongs. The oil temperature will drop; adjust the heat as necessary to maintain a temperature between 300 degrees F and 325 degrees F. Fry the chicken until the coating is crisp but not browned, about 6 minutes. Remove to a rack set on a baking sheet to drain. (The chicken will not be fully cooked at this stage.) Let the oil temperature return to 350 degrees F before frying the remaining chicken.
Double-fry the chicken: Increase the oil temperature to 375 degrees F. Working in two batches, fry the chicken again until the coating is browned and very crisp, 4 to 6 minutes for wings and 6 to 8 minutes for drumsticks. Adjust the heat as necessary to maintain a temperature of 350 degrees F. Remove with tongs and transfer to a clean rack set on a baking sheet; brush all over with the sauce. Sprinkle with sesame seeds.