In a large, deep skillet or Dutch oven, swirl oil to coat. Season chicken all over with salt and arrange in cold skillet skin side down. Cook over medium heat, undisturbed, until skin is golden and crispy and easily releases from skillet, about 10 minutes. Flip chicken and cook just until browned on the bottom, 1 to 2 minutes more. Transfer to a plate.

In the same skillet over medium heat, cook ginger and garlic, stirring, until fragrant, about 1 minute. Add brown sugar, soy sauce, and ½ cup water and stir until sugar is dissolved. Return chicken to skillet skin side up.

Bring to a boil over medium-high heat. Reduce heat to medium-low to maintain a simmer, then cover and cook until chicken is cooked through and an instant-read thermometer inserted into the center registers 165°, 13 to 18 minutes.

Transfer chicken to a clean plate. Bring sauce to a boil over medium-high heat, then reduce heat to medium-low and simmer, stirring occasionally, until slightly thickened and deep brown in color, 2 to 3 minutes.

Meanwhile, in a small bowl, whisk cornstarch with remaining 1 Tbsp. cold water. Add to sauce and stir until thickened to a glaze, about 1 minute.

Return chicken to pot and toss to coat in glaze. Top with scallions if using.