In a small bowl, combine the butter, thyme, lemon zest, garlic and a generous pinch of salt and mash with a fork or spoon until well blended.
Put several large handfuls of the spinach in a large nonstick skillet. Season with a sprinkle of salt. Turn the heat to medium-high and cook, stirring frequently, until the spinach is mostly wilted, 1 to 2 minutes. Add another few handfuls of spinach and another sprinkle of salt, and continue to cook, tossing until wilted. Repeat until all of the spinach is wilted.
Turn off the heat, but leave the pan on the burner. Add the butter mixture and toss just until it melts and coats the spinach. Season to taste with salt, as desired, and serve immediately.