Preheat the oven to 350 degrees F. Lightly oil a 1-quart baking dish.
Whisk the heavy cream, 1 teaspoon salt, a few grinds of pepper and the nutmeg together in a small bowl. Set aside.
Heat the oil in a large skillet over medium heat. Add the scallions and garlic. Cook, stirring, until the garlic is fragrant and the scallions are soft, about 2 minutes. Add the spinach and artichokes and cook, stirring, until the spinach wilts, about 3 minutes. Add the cream cheese and stir until melted, about 1 minute.
Remove the skillet from the heat and stir in the heavy cream mixture. Transfer it to the prepared dish and sprinkle the Parmesan on top. Bake until the center of the dip is just set and the edges are golden brown, about 30 minutes. Serve warm or at room temperature with toasted bread or crackers.
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