Step 1

Preheat the oven to 375 degrees F. Season the chicken with 1/2 teaspoon salt, and pepper to taste. Heat a medium skillet over medium-high heat; add 1/2 tablespoon vegetable oil, then add the chicken, skin-side down, and cook until the skin is golden brown, about 6 minutes. Transfer to a rimmed baking sheet, skin-side up; reserve the skillet.

Step 2

Toss the mushrooms with the remaining 1/2 tablespoon vegetable oil and season with salt and pepper; scatter around the chicken on the baking sheet. Bake until the mushrooms are tender and a thermometer inserted into the thickest part of the chicken registers 160 degrees F, about 25 minutes.

Step 3

Meanwhile, melt the butter in the reserved skillet over medium heat. Add the flour and cook, stirring, 1 minute. Add the chicken broth and bring to a simmer, whisking. Add the wine, sugar and 1/4 teaspoon salt and simmer until the sauce is reduced by half, about 10 minutes. Season with salt and pepper.

Step 4

Spoon some of the red wine sauce onto each plate; top with the chicken and mushrooms.