1. Stir together miso, wine, brown sugar, sesame oil, and 1 1/2 teaspoons ginger. Rub mixture all over chicken and under skin; let stand 1 hour. Preheat oven to 450 degrees with rack in upper third. Place chicken, skin-side up, on a lightly oiled rimmed baking sheet; roast until a thermometer inserted in thickest part of breasts (avoiding bone) registers 135 degrees, 12 to 14 minutes. Increase heat to broil and cook, rotating pan, until skin is crisp and thermometer registers 160 degrees, 3 to 4 minutes more. Let rest 15 minutes; remove meat from bones and slice crosswise.

2. Bring stock and mushrooms to a boil in a medium pot, then reduce heat and simmer until mushrooms are tender, about 15 minutes. Stir in remaining 1 tablespoon ginger and tamari; season with salt. In another pot, cook udon in salted boiling water according to package instructions; drain and rinse. Divide udon, broth, and mushrooms among bowls. Top with chicken, watercress, and scallions; serve, with daikon.