Pound garlic, cilantro stems, white peppercorns, coriander seeds, and cumin seeds in a mortar into a fine, fragrant paste.
Whisk the spice paste, fish sauce, soy sauce, brown sugar, and cold water in a large bowl until sugar dissolves.
Toss chicken pieces in the marinade, cover, and refrigerate for at least 4 hours or overnight.⏱ 240 min
Toss thinly sliced shallots with 1 tablespoon rice flour and a pinch of salt until lightly coated.
Heat 2 inches of neutral oil in a heavy Dutch oven or wok to 325°F (165°C).
Fry shallots, stirring continuously, until pale golden and crisp, about 3 to 5 minutes; drain on paper towels.⏱ 5 min
Stir the remaining rice flour and cornstarch directly into the marinated chicken bowl until a light batter clings to each piece.
Increase oil heat to 350°F (175°C) in the same Dutch oven.
Lower chicken into hot oil in batches, frying until deep golden and cooked through, about 10 to 12 minutes.⏱ 12 min
Transfer fried chicken to a wire rack and let rest for 3 minutes.⏱ 3 min
Pile hot chicken high on a platter, smother generously with crispy shallots, and serve with sweet chili dipping sauce.