Position a rack in the upper third of the oven and preheat to 425 degrees . In a saucepan, combine the potatoes with salted water to cover by 1 inch. Bring to a boil and cook until tender, 12 to 15 minutes. Drain, reserving 1 cup of the cooking water; return the potatoes to the pot. Mash with the cream until smooth; season with salt.
In a large nonstick skillet, heat the olive oil over high heat. Add the mushrooms and cook, stirring occasionally, until golden, about 5 minutes; transfer to a plate. Crumble the beef evenly across the pan and cook, undisturbed, until the liquid cooks off and the meat begins to brown, 3 to 4 minutes. Lower the heat to medium and stir in the finely chopped scallions, the poblano, 1 teaspoon salt and 1/2 teaspoon pepper; cook, stirring, for 2 minutes. Stir in the reserved mushrooms, 1/4 cup mashed potatoes and the reserved 1 cup cooking water. Lower the heat and simmer until the juices are thickened, about 3 minutes. Season with salt and pepper.
Spread slightly more than half of the potatoes evenly in a greased 9-by-11-inch baking dish. Spoon the meat mixture evenly on top, then spoon the remaining mashed potatoes evenly across the filling to enclose. Bake until lightly golden, 20 to 25 minutes. Sprinkle with the sliced scallions; let stand for 10 minutes before serving.