Bring a large pot of salted water to a boil. Fill a medium bowl with ice water and add a generous pinch of salt.
Add the spinach to the pot and cook until tender but still bright green, 3 to 4 minutes. Drain well, then transfer to the bowl of ice water until cool. Drain well again, transfer to a clean dish towel and squeeze out any excess water. Finely chop and set aside.
Melt 1 tablespoon of the butter in a medium saucepot over medium heat. Add the flour and cook, stirring constantly, until light brown, about 2 minutes. Gradually whisk in 1 1/2 cups of the milk. Continue to cook, whisking constantly, until the mixture comes to a boil. Reduce the heat to low and simmer, whisking occasionally, until the sauce is thickened, about 10 minutes.
Stir in the spinach, cayenne, cloves, nutmeg, the remaining 1 tablespoon butter, 3/4 teaspoon salt and a few grinds of pepper until combined. Cook until heated through, adding the remaining 1/2 cup milk if the sauce is too thick. Adjust the seasoning with additional salt and pepper.
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