Wash the spinach thoroughly using 2 or 3 changes of water, but don’t dry the leaves. Set a 6- to 8-quart Dutch oven over medium-high heat and add half of the wet spinach to it. Season with 1/4 tsp. salt, cover, and steam, tossing frequently, until wilted, 3 to 4 minutes. Transfer to a colander in the sink and repeat with the remaining spinach.
Allow the spinach to cool in the colander for several minutes. Using a clean, folded dishtowel, press down on the spinach to remove as much water as possible. Let the spinach rest for a few more minutes and then press again to remove more water. Transfer the spinach to a cutting board, blot again with the towel, and chop very coarsely.
Put the milk, cream, and smashed garlic in a 1-quart saucepan. Bring to a boil over medium heat; then immediately remove from the heat and let sit for 10 minutes.
With a fork, remove most of the smashed garlic from the cream mixture, pressing the garlic against the side of the pan to squeeze out the cream. (It’s fine if small pieces of garlic remain.) Transfer the cream mixture to a liquid measuring cup and add 1/2 tsp. salt, a few grinds of pepper, and a big pinch of nutmeg.
Wipe out the saucepan. Melt the butter in the pan over medium-low heat. Add the flour and cook, whisking constantly, until pale and smooth, about 1 minute.
Whisk in the cream mixture in a slow, steady stream. Raise the heat to medium and simmer the sauce, whisking constantly, until it thickens and reduces slightly, about 2 minutes. Remove from the heat.
Return the chopped cooked spinach to the Dutch oven and set over medium heat. Add the sauce and stir to combine. Add the Parmigiano and mix well. Continue to stir constantly until the spinach is hot, 1 to 2 minutes. Season with more salt and pepper and serve immediately.