Season the chicken with salt and pepper. Heat 1 tablespoon vegetable oil in a large skillet over medium-high heat. Add the chicken skin-side down and cook until browned and crisp, 7 to 10 minutes. Flip and cook until browned on the other side, about 5 more minutes. Remove the chicken to a plate.
Wipe out the skillet. Add the remaining 1 tablespoon vegetable oil and heat over medium-high heat. Add the mushrooms, season with salt and cook, stirring occasionally, until lightly browned around the edges, about 5 minutes.
Meanwhile, whisk 3/4 cup water, the oyster sauce, soy sauce, sesame oil and ginger in a small bowl. Return the chicken skin-side up to the skillet; add the oyster sauce mixture and bring to a boil. Reduce the heat to a gentle simmer, cover and cook until the chicken is cooked through and the sauce is slightly reduced, about 7 minutes. Add the sausage and cook until warmed through, about 1 minute. Stir in the scallions.
Divide the chicken and sauce among plates. Serve with rice.
Chinese sausage is a hard sausage with a sweet-smoky flavor. If you can?t find it, use maple bacon.