Cook the spinach according to package directions. Once cooked, drain in a colander, and press with the back of a large spoon to remove excess moisture. Set aside.
Heat 1 tablespoon of the oil in a medium saucepan over medium heat. Add the onion and cook, stirring frequently, until softened, about 5 minutes. Add the remaining 2 tablespoons of olive oil and the flour and whisk constantly until the mixture is smooth and golden, about 2 minutes.
Whisk the milk, salt, pepper, and nutmeg slowly into the flour mixture. Raise the heat and bring to a low boil, stirring constantly. Reduce the heat and continue to simmer and stir gently until the mixture thickens, about 3 minutes.
Turn off the heat and whisk in the Parmesan cheese and cream cheese until the cream cheese melts. Stir in the cooked spinach, and season with additional salt, pepper, and nutmeg to taste. Place over low heat and reheat if necessary.