Melt the butter in a saucepan over medium heat.

Whisk in the flour until smooth; cook, stirring, until the mixture lightens, about 1 minute.

Remove from the heat; whisk in the milk, 2 teaspoons salt and the nutmeg.

Return to medium heat and bring to a boil, whisking.

Remove from the heat again; stir to cool slightly.

Heat a deep skillet over medium heat.

Add the spinach and 1 teaspoon salt; cover and cook about 3 minutes.

Toss with tongs, then continue to wilt, uncovered, about 2 more minutes. Drain and cool slightly, then squeeze the spinach until dry.

Coarsely chop.

Gently reheat the sauce, then whisk in the whole egg and yolks; cook, stirring, until the sauce thickens.

Stir in the spinach; heat through. Season with salt and pepper.