In a large, shallow baking dish, stir 2 tablespoons of the brown sugar with 2 tablespoons of the fish sauce until the sugar is dissolved. Add the chicken legs and coat them thoroughly with the marinade. Let the chicken stand at room temperature for 2 hours or refrigerate overnight.
Preheat the oven to 450°. In a small saucepan, heat the vegetable oil. Add the scallions and cook over high heat until they sizzle, about 30 seconds. Remove from the heat.
Meanwhile, in a medium enameled cast-iron casserole, combine the remaining 1/2 cup of brown sugar with 1 tablespoon of water and cook over moderately high heat, stirring a few times, until bubbling, about 3 minutes. Gradually stir in 1 1/2 cups of water, then stir in the remaining 1/3 cup of fish sauce along with the soy sauce, vinegar, honey and half of the scallion oil. Bring to a boil and simmer over moderately high heat until slightly reduced, about 5 minutes. Add the shallots, garlic, ginger and chiles and simmer over moderately low heat for 5 minutes.
Roast the chicken legs in the upper third of the oven for about 15 minutes, until they are browned.
Discard the chicken skin and nestle the legs in the sauce in the casserole. Tuck in the pickled daikon slices. Cover and simmer over low heat for about 15 minutes, basting the chicken a few times, until cooked through; add a few tablespoons of water if the sauce gets too thick and dark.
Meanwhile, in a wide stainless steel or bamboo steamer, bring 1 1/2 inches of water to a boil. Moisten a double layer of cheesecloth that is large enough to cover the steamer basket and reach part of the way up the side; line the steamer basket with it. Add the drained rice to the basket and pat into an even layer. Cover and steam the rice over moderate heat for about 15 minutes, until tender.
Uncover the rice and season lightly with salt. Spoon the remaining scallion oil over the rice and stir gently. Serve the chicken with the sticky rice.