Rinse the drumsticks and pat them dry with paper towels; set aside.
Trim about 2 inches (5 cm) off the bottom of the cilantro stems. Pound the stems in a mortar and pestle to release their liquid, then squeeze the crushed stems by hand to extract any remaining juice; measure 1 tablespoon.
In a large bowl, whisk together the shrimp sauce, sugar, egg white, sesame oil, cilantro stem juice, cornstarch, and all-purpose flour until smooth and free of lumps.
Add the chicken to the bowl and toss to coat each piece thoroughly in the marinade.
Cover and marinate the coated chicken in the refrigerator for at least 4 to 6 hours.
When ready to cook, heat oil in a deep fryer or large pot to medium-high heat (about 350°F/175°C).
Carefully lower the marinated drumsticks into the hot oil in batches, and deep-fry until the exterior is crispy and golden brown and the internal temperature reaches 165°F (75°C), about 8–12 minutes per batch depending on size.
Transfer the fried chicken to a plate lined with paper towels to drain excess oil, then serve immediately with chili sauce on the side if desired.
