Place the potatoes in a pot and cover with a generous amount of cold water. Bring to a boil over high heat, then reduce the heat until the water is simmering (small bubbles should just be breaking on the surface). Simmer the potatoes until very tender, 18 to 20 minutes.
White the potatoes are cooking combine the wine (or stock), tarragon (or thyme), and garlic in a small pot, bring to a boil over high heat, and reduce by half, about 2 minutes. Pour in the cream, bring to a simmer, and reduce until the sauce lightly thickens 3 to 4 minutes. Stir in the mustard. Cover and keep warm over low heat.
Drain the potatoes well and, using a potato masher, mash thoroughly. Add the buttermilk and butter and beat until well combined. Season with salt and pepper, then stir in the green onions.
To serve, mound a scoop of the potatoes in the center of each dinner plate. Arrange the chicken on and around the potatoes, then drizzle with the mustard sauce. Enjoy.
Servings 4