Step 1Toss the chicken with the onion and garlic and marinate for at least 30 minutes in the refrigerator.
Step 2In a medium bowl, whisk together the cornstarch, salt and pepper, then whisk in the egg and cold water, being careful not to over-mix.
Step 3Heat the oil in a deep, heavy saucepan over medium heat. Use enough oil that it will cover the chicken pieces by at least an inch when you add them. Heat to a temperature of 350 degrees.
Step 4Using long chopsticks or tongs, dip one chicken piece at a time in the cornstarch mixture and carefully place it in the hot oil. Repeat with more chicken, but be careful not to crowd the pan (the chicken pieces should not touch one another); the frying will need to be done in batches. Fry the chicken until crisp and golden brown, 8 to 10 minutes. (Check a large piece by breaking it open; it should be firm throughout and the juices should run clear.) Drain the chicken on paper towels and repeat until all of the chicken is fried.
Step 5While the chicken is frying, make the seasoning sauce: In a small saucepan, combine the chile paste, sugar, ketchup and lemon juice. Heat the mixture over medium heat to bring to a simmer, adding just enough water to thin the sauce to a glaze-like consistency. Simmer for 2 to 3 minutes to deepen the flavors, then remove from heat. Stir in the toasted sesame seeds and set aside.
Step 6When all of the chicken is fried, quickly fry the pieces once more to a rich golden-brown for added crispness. Toss the fried chicken with the sauce and serve immediately.