Heat oven to 425 degrees. Pat chicken thoroughly dry with paper towels and sprinkle all sides with 2 teaspoons salt.

Coat a large, high-sided skillet or Dutch oven with 1 tablespoon oil. Arrange chicken, skin side down, in a single layer in the cold skillet and place over medium heat. Cook, undisturbed, until the skin is browned and releases easily from the pan, about 15 minutes.

While the chicken cooks, cut potatoes into 1-inch-thick chunks and place in a large bowl. Chop the rosemary and anchovy, smash and peel the garlic, then add to the bowl. Add the capers, 2 tablespoons oil and ½ teaspoon salt; toss to combine.

Flip the chicken, then add the potato mixture to the skillet, tucking the pieces around and under the chicken. Pour the wine over the potatoes. Transfer the skillet to the oven and roast, uncovered, until the chicken is cooked through and the potatoes are tender, about 25 minutes.

Return the skillet to the stove. Transfer the chicken to a plate to rest. Add the vinegar and 2 tablespoons water to the skillet and continue to cook the potatoes over medium heat, stirring occasionally, until coated with a thickened, glossy sauce, about 5 minutes. If the sauce seems too thick or oily, stir in water 1 tablespoon at a time to help emulsify the sauce and achieve desired consistency. Taste and add salt and more vinegar, as needed.

Return the chicken to the skillet and sprinkle parsley over everything to serve.