Arrange a rack in center of oven; preheat to 425°. In a large, deep, ovenproof skillet over high heat, heat vegetable oil. Season chicken with salt and pepper. Add chicken to skillet skin side down and cook, turning halfway through, until deeply golden, about 6 minutes per side. Transfer to a plate.
In same skillet over medium-high heat, cook shallots, ginger, and garlic, stirring, until fragrant, about 1 minute. Add wine and cook, stirring frequently, until reduced by about half, about 3 minutes. Add water, soy sauce, and sugar and bring to a boil. Nestle chicken skin side up in skillet, tucking in between shallots.
Transfer skillet to oven and braise chicken, uncovered, until an instant-read thermometer inserted into thickest part registers 165°, about 35 minutes.
Transfer chicken to a platter. Return skillet to high heat and cook, stirring occasionally, until sauce is thickened, about 3 minutes. Pour sauce and sesame oil over chicken.
Top with sesame seeds and scallions. Serve with rice alongside.