Heat oven to 425° F. On a rimmed baking sheet, toss the potatoes with 1 tablespoon of the oil, ½ teaspoon salt, and ¼ teaspoon pepper. Roast, tossing once, until golden brown and tender, 20 to 25 minutes.
Meanwhile, heat the remaining tablespoon of oil in a large skillet over medium-high heat. Season the chicken with ½ teaspoon salt and ¼ teaspoon pepper; cook until golden brown and cooked through, 6 to 7 minutes per side.
In a second large skillet, cook the bacon over medium heat until crisp, 5 to 7 minutes; remove. Add the shallot, mustard, and vinegar to the drippings in the pan and cook, stirring frequently, until the shallot is soft, 2 minutes. Add the cabbage and cook, tossing, until wilted, 2 to 4 minutes more. Serve with the chicken and sprinkle with the bacon.