Heat the olive oil in a 12-inch skillet over medium-high heat. Add the shallots and 1/2 tsp. salt. Cook, stirring frequently, until soft and golden, 5 to 6 minutes.
Add the potatoes, wine, 1 tsp. salt, a few grinds of pepper, and 1-1/2 tsp. water. The potatoes should be nearly submerged. Bring to a boil, cover partially, reduce the heat to medium low, and simmer, stirring about every 10 minutes, until the potatoes are tender when pierced with a fork and the liquid is reduced to a slightly thick sauce, bout 45 minutes. If the liquid cooks away too fast, add water as needed.
With a potato masher, smash the potatoes just enough to break some and leave others intact. Stir together the potatoes and sauce and season to taste with more salt or pepper. Serve sprinkled with the parsley and dotted with the butter.
Make Ahead Tips
You can make the potatoes up to two hours ahead; cover with foil and keep in a warm spot until ready to serve.
nutrition information (per serving): Calories (kcal): 190; Fat (g): 7; Fat Calories (kcal): 60; Saturated Fat (g): 2; Protein (g): 3; Monounsaturated Fat (g): 4; Carbohydrates (g): 26; Polyunsaturated Fat (g): 0.5; Sodium (mg): 310; Cholesterol (mg): 5; Fiber (g): 2;