How to Make It
In a saucepan, cover the potatoes with water and bring to a boil. Add a pinch of salt and simmer over moderate heat until tender, 20 minutes; drain well. Pass the potatoes through a ricer back into the saucepan. Stir in the nutmeg, 1/2 cup of the cream and 4 tablespoons of butter over low heat until incorporated. Season with salt and pepper; keep warm.
Meanwhile, in a small saucepan, heat 1 tablespoon of the oil. Add the shallot and cook over moderate heat until softened, 2 minutes. Add the broth and wine and simmer until reduced to 1/2 cup, 5 minutes. Whisk in the mustard and remaining 1/2 cup of cream and bring to a boil. Remove from the heat and whisk in the remaining 4 tablespoons of butter. Season with salt and pepper; keep warm.
Meanwhile, bring a large, deep skillet of water to a simmer and add a pinch of salt. One at a time, crack an egg into a small bowl and slide it into the water. Poach the eggs until the whites are firm and the yolks are still runny, 3 minutes. Using a slotted spoon, transfer the eggs to a paper towel-lined plate to drain.
In a bowl, toss the spinach, lemon juice and remaining 1 tablespoon of oil and season with salt and pepper. Mound the potato puree on plates. Set the eggs on top and spoon the sauce over. Pile the spinach on the side and serve.