Bring a large pot of salted water to a boil. Add the spinach and cook for 2 minutes. Drain in a fine-mesh strainer, pressing with a large spoon to release as much water as possible. Finely chop and set aside.

Bring the cream to a low boil in a small saucepan. Remove from the heat.

Melt the butter in medium-heavy saucepan over medium-high heat. Add the shallots and garlic and cook, stirring, until soft, about 1 minute. Add the flour and cook, and then reduce the heat to low and cook, stirring constantly with a heavy wooden spoon, until a light blond roux forms, 2 to 3 minutes. Add the milk in a steady stream, whisking constantly, and cook until thick and smooth, 1 to 2 minutes. Add the salt, white pepper and nutmeg and simmer until thickened, 3 to 5 minutes. Add the hot cream, whisking constantly, and cook for 1 minute. Fold in the Swiss and Parmesan cheeses, and mix until smooth. Add the spinach, mix well and cook until completely warmed through, 1 to 2 minutes.

Remove from the heat and adjust the seasoning, to taste. Serve hot.